Observation of anomalous decay of a polarized three-component Fermi gas

Abstract

Fermionic systems with multiple internal states, such as quarks in quantum chromodynamics and nucleons in nuclear matter, are at the heart of some of the most complex quantum many-body problems. The stability of such many-body multi-component systems is crucial to understanding, for instance, baryon formation and the nuclear structure, but these problems are typically challenging to tackle theoretically. Versatile experimental platforms on which to study analogous problems are thus sought-after. Here, we create a uniform three-component Fermi gas with controllable polarization, and observe anomalous decay of the polarized gas, in which the loss rates of each component unexpectedly differ, contradicting generic assumptions of three-body losses in this system. We introduce a generalized three-body rate equation which captures the decay dynamics, but the underlying microscopic mechanism is unknown.

Introduction

Characterizing whether—and into what—a system’s state decays has often been a pathway to discovering new quantum phenomena. Such stability problems are ubiquitous in many-body physics, ranging from the onset of turbulence in quantum liquids¹ to dissipation processes in Josephson junctions², to the stability of nuclei³. Ultracold atomic systems have been a fertile ground for such studies: their (in)stability has revealed a wide range of interesting and sometimes unexpected phenomena, such as quantum-fluctuation stabilization against many-body collapse⁴ and prethermalization of metastable phases⁵. Notably, three-body recombination losses have revealed few-body physics^6,7, including threshold laws^8,9, the Efimov effect^10,11, and state-resolved quantum chemistry¹². There has been renewed appreciation that the stability of quantum gases against inelastic-collision losses^13,14 (or lack thereof) is also a pristine probe of many-body quantum correlations^15,16,17,18.

Strongly interacting fermions with contact interactions have been a fruitful platform for stability studies. The discovery of long-lived pairs in the two-component (‘spin-1/2’) Fermi gas^{19,20,21,22,23} unlocked the field of the BEC-BCS crossover²⁴. Three-component (‘spin-1’) fermions could give access to even richer physics, such as quantum chromodynamics-like phenomena and complex pairing patterns^{25,26,27,28,29,30,31,32}. Pioneering experiments showed that unpolarized (i.e., spin-population balanced) gases of three-component fermions exhibit interesting decay behavior related to the Efimov effect^{33,34,35,36,37,38}. However, density-dependent losses in those spatially inhomogeneous gases were unavoidably coupled to particle transport and heating, making the interpretation of those experiments challenging. Our understanding of the metastability of the three-component Fermi gas is currently limited.

Results

In this work, we create box-trapped gases of three-component fermions with controllable spin-population imbalance, and we study their stability (see Fig. 1a). Such spatially homogeneous gases are more amenable to the study of complex dynamics, as they obey cleaner dynamics than their inhomogeneous counterparts (see e.g.^16,39,40,41). This has enabled us to observe a surprising violation of the generic expectation that loss rates among spin components should be equal in a three-body process involving all three components. We rule out credible explanations for this effect, suggesting that unexpected physics is at play.

Fig. 1: Preparation of a homogeneous three-component Fermi gas.

a Top: Sketch of the optical box. Bottom: The stability of the mixture is studied by measuring the density of each spin population over time. b Top: Breit-Rabi diagram of the lowest hyperfine states of ⁶Li. The three (pseudo)-spins are encoded in the three lowest states, respectively $\left\vert 1\right\rangle$, $\left\vert 2\right\rangle$ and $\left\vert 3\right\rangle$ (identified by the same colors throughout this work). The polarization of the three-component mixture is controlled via radio-frequency (RF) pulses. Bottom: Scattering length a_ij for each pair of spin states $\left\vert i\right\rangle$-$\left\vert \, j\right\rangle$ (in units of the Bohr radius a₀); adjacent colors match the corresponding pair of states. Vertical dash-dotted lines show the locations of the broad Feshbach resonances B_ij: B₁₂ ≈ 832 G, B₁₃ ≈ 690 G, B₂₃ ≈ 810 G (for more details, see ref. ⁶⁴). c Top: In situ absorption images of a typical polarized three-component mixture (averaged over 10 realizations), taken along the z axis; the color scale corresponds to the optical density (OD). The length and radii of this (slightly) conical box are L = 120(2) μm, R₁ = 75(1) μm and R₂ = 73(1) μm, and its trap depth is U_box = k_B × 1.6(2) μK, where k_B is Boltzmann’s constant; note that boxes of various sizes were used in this work. Throughout this work, the displayed uncertainties (one standard deviation) denote statistical errors only. Bottom: Integrated density along the x and y axes for each component with fits to homogeneous density profiles (dotted lines, see “Methods”).

Our experiment begins with a gas of ⁶Li atoms in a red-detuned crossed optical dipole trap. Depending on the spin polarization and magnetic field B studied, we use various preparation sequences (see “Methods”). In general, our gases are prepared in an incoherent mixture of two of the three lowest Zeeman sublevels, which encode the three (pseudo-)spin components of our ‘spin-1’ fermions (respectively labeled $\left\vert 1\right\rangle$, $\left\vert 2\right\rangle$, and $\left\vert 3\right\rangle$, see the top panel of Fig. 1b). This two-component mixture is evaporatively cooled at a bias magnetic field B₀ (which depends on the two spin states used) and loaded into a blue-detuned optical box trap of wavelength 639 nm. As an example, in a typical sequence we evaporate a balanced mixture of $\left\vert 1\right\rangle$-$\left\vert 3\right\rangle$ at B₀ ≈ 690 G, achieving N₁ ≈ N₃ ≈ 5 × 10⁵ at T/T_F ≈ 0.25, where N_j is the number of atoms of spin $\left\vert \, j\right\rangle$ and T_F ≈ 400 nK is the Fermi temperature.

We ramp the magnetic field to the field of interest B in 200 ms; this time is slow compared to the two-body collision rate but fast compared to the lifetime of the two-component mixtures in the range of fields investigated (see “Methods”). We let the magnetic field settle for 100 ms and prepare the spin mixtures by sequentially applying variable radio-frequency (RF) pulses to drive the $\left\vert 1\right\rangle$-$\left\vert 2\right\rangle$ and $\left\vert 2\right\rangle$-$\left\vert 3\right\rangle$ transitions (top panel of Fig. 1b). The fermions interact via binary contact interactions, characterized by an s-wave scattering length a_ij for each pair of spin states $\left\vert i\right\rangle$-$\left\vert \, j\right\rangle$. The value of B sets a_ij, allowing us to explore different interaction regimes, including the Feshbach resonances (where a_ij diverges⁴², see bottom panel of Fig. 1b).

We hold the gas for a variable time t before measuring N_j. Typical in situ absorption images of each spin population in an imbalanced mixture are shown in Fig. 1c (top panel), together with integrated column densities along the two directions x and y (bottom panel). For the range of B explored in this work (deep in the Paschen-Back regime for ⁶Li), all three spins are nearly identically levitated against gravity using a magnetic field gradient (see “Methods”). The integrated density profiles of the three components show that their densities are spatially uniform.

We first study the stability of spin-balanced samples, N₁ ≈ N₂ ≈ N₃, at B = 845 G (near the Feshbach resonance of the $\left\vert 1\right\rangle$-$\left\vert 2\right\rangle$ states at 832 G, see the bottom panel of Fig. 1b). A typical decay of an unpolarized gas is shown in Fig. 2a. As all two-component mixtures are stable at this magnetic field (see “Methods”), it is natural to expect that the losses are dominated by three-body recombinations involving all three components and releasing enough energy to kick all participating particles from the trap. As per that expectation, we find that initially unpolarized mixtures remain indeed unpolarized (as was previously observed in inhomogeneous gases^33,34). However, the density uniformity of our samples enables us to go further and model-independently confirm the basic mechanism at play. In the inset of Fig. 2a, we show the total atom loss rate $\dot{N}\equiv {{{\rm{d}}}}N/{{{\rm{d}}}}t$ as a function of the total atom number N ≡ N₁ + N₂ + N₃. The data is well captured by a power law $\dot{N}\propto -{N}^{\gamma }$. For a homogeneous unpolarized gas with a total density n = N/V and a constant volume V, this implies that $\dot{n}\propto -{n}^{\gamma }$. Importantly, the exponent γ encodes information on the number of independent particles involved in each loss event⁴³. For the spin-balanced decay at 845 G, we observe γ = 2.9(1), consistent with losses dominated by energy-independent recombination involving three distinguishable fermions. As all scattering lengths are negative at B = 845 G, there are no universal two-body bound states, and the losses are expected to be recombinations to deeply bound (non-universal) states^44,45.

Fig. 2: Anomalous losses in a polarized three-component Fermi gas.

a Typical decay of an unpolarized gas at 845 G. The red line is a fit to Eq. (1); t = 0 corresponds to the end of the RF pulses. Inset: Total loss rate $| \dot{N}|$ versus N. The solid blue line is a power-law fit yielding γ. The error bars are the standard deviations of three measurements and are smaller than the marker size. We estimate an additional systematic error of 10% on γ (see “Methods”). b Decay of a polarized gas at 845 G. In the main panel, the solid curve is a solution to Eq. (1), where L₃ is fixed to the value measured in the unpolarized decay, L₃(B = 845 G) = 2.4(1) × 10⁻²⁰ cm⁶/s. The error bars are the standard deviations of three measurements and are smaller than the marker size. Inset: Decay of an inhomogeneous (harmonically trapped) polarized gas at 845 G; here, the red solid curve is a guide to the eye. Initial numbers for the box (resp. harmonic) trap data are given on the right (resp. left) column of the table, see circle (resp. diamond) symbols. The error bars are the standard deviations of approximately eight measurements. c Typical decay of an unpolarized gas at 690 G. The red line is a fit to Eq. (1). The error bars are the standard deviations of three measurements and are smaller than the marker size. Inset: Total loss rate $| \dot{N}|$ versus N. d Decay of a polarized gas at 690 G. The solid curves are fits to Eq. (3). L₃ is fixed to the value measured in the unpolarized decay ${L}_{3}^{0}=1.1(2)\times 1{0}^{-21}\,{{{{\rm{cm}}}}}^{6}/{{{\rm{s}}}}$ (see caption of Fig. 3). The error bars are the standard deviations of three measurements and are smaller than the marker size. Inset: Decay of a corresponding inhomogeneous polarized gas at the same field. The error bars are the standard deviations of three measurements. In (c, d), early times (open symbols) are excluded from our analysis (see Fig. S1 in Supplementary Information).

More interestingly, we can access this decay dynamics in the previously unexplored case of the polarized gas. In Fig. 2b, we show a typical decay of a polarized sample at the same field B = 845 G. Notably, the losses $\Delta {N}_{j}\equiv {N}_{j}(t)-{N}_{j}^{{{{\rm{initial}}}}}$ are the same for all spins throughout the decay. This is unsurprising as the loss rate equation for each spin component in an uncorrelated uniform gas is expected to take the form

$${\dot{n}}_{j}=-{L}_{3}{n}_{1}{n}_{2}{n}_{3},$$

(1)

where L₃ is the (density-independent) three-body recombination loss coefficient. We compare the data with the solution of Eq. (1), with L₃ fixed to the value measured from the decay of the unpolarized gas; we find excellent agreement using only the initial densities as fitting parameters.

In fact, that the losses are the same for all spin components is a more general expectation. First, we performed the same measurement with harmonically trapped polarized samples (in the crossed optical trap that precedes the loading of the box), and arrive at the same qualitative conclusion (see inset of Fig. 2b). Indeed, in a spatially inhomogeneous sample, the losses $\Delta {N}_{j}=\int{{{\rm{d}}}}t{{{\rm{d}}}}{{{\bf{r}}}}\,{\dot{n}}_{j}({{{\bf{r}}}})-{N}_{j}^{{{{\rm{initial}}}}}$ would remain equal, regardless of the respective density distributions for the spin populations if Eq. (1) remains locally valid. Secondly, calculating ${\dot{n}}_{j}$ under the assumptions that no spin-changing collisions occur and that losses are due to local three-body recombination yields⁴⁶ ${\dot{n}}_{j}\propto - {\sum}_{\alpha }\langle {a}_{3,\alpha }^{{{\dagger}} }{a}_{2,\alpha }^{{{\dagger}} }{a}_{1,\alpha }^{{{\dagger}} }{a}_{1,\alpha }{a}_{2,\alpha }{a}_{3,\alpha }\rangle$, where a_j,α (resp. ${a}_{j,\alpha }^{{{\dagger}} }$) is the annihilation (resp. creation) operator for state $\left\vert \, j\right\rangle$ at position α (see “Methods”). We thus see that the loss rates are spin-independent even in the presence of an inhomogeneous trap, or nontrivial quantum correlations that would preclude factoring the 6-operator expectation value into a product of densities.

We now turn to the field B = 690 G, the location of the Feshbach resonance of the pair $\left\vert 1\right\rangle$-$\left\vert 3\right\rangle$. In Fig. 2c, we show the decay of the unpolarized gas. Its behavior is qualitatively the same as the B = 845 G case. Indeed, the gas remains unpolarized and the loss scaling $\dot{n}\propto -{n}^{2.8(1)}$ is also consistent with three-body dominated losses (Fig. 2c inset); even after the total density has decayed by about 90%, any imbalance is very small as all concentrations are within 4% of the balanced mixture (even more stringent than the previous similar observation in harmonically trapped gases^33,34); see Fig. S5 in Supplementary Information for a more detailed discussion. However, the polarized gas at B = 690 G yields a major qualitative surprise: the loss rates per spin are distinct, with the majority component showing significantly larger losses (Fig. 2d). Importantly, this anomaly is not specific to the box-trapped system; indeed, inhomogeneous samples also exhibit this effect, see inset of Fig. 2d. This violates the basic expectation that the loss rates should be equal in a three-body recombination process involving all three spin states. Note that at this field the scattering lengths between $\left\vert 1\right\rangle$-$\left\vert 2\right\rangle$ and $\left\vert 2\right\rangle$-$\left\vert 3\right\rangle$ are relatively small and positive (a₁₂ ≈ 1400a₀ and a₂₃ ≈ 1150a₀, where a₀ is the Bohr radius). Therefore, universal two-body bound states exist, the Feshbach dimers $\left\vert 12\right\rangle$ and $\left\vert 23\right\rangle$, with binding energies ϵ_b ≈ k_B × 15 μK and  ≈ k_B × 23 μK respectively (see Fig. S2 in Supplementary Information). Furthermore, losses are expected to be dominated by three-body recombination into these states^44,45.

Notwithstanding this unexpected behavior, we observe that the total loss rate still obeys the expected three-body rate equation $\dot{n}=-3{L}_{3}{n}_{1}{n}_{2}{n}_{3}$, see orange points in Fig. 3a. Moreover, the extracted L₃ is consistent with the unpolarized gas value (blue points).

Fig. 3: Stability of the polarized three-component Fermi gas.

a Total loss rate $| \dot{n}|$ versus n₁n₂n₃, for both unpolarized (blue) and polarized (orange) gases at 690 G, averaged over 23 experiments (the data shown excludes the hatched region of (b)). The error bars are the standard deviations of the 23 sets of measurements. Colored bands are linear fits to the equation $\dot{n}=-3{L}_{3}{n}_{1}{n}_{2}{n}_{3}$ including one standard deviation statistical uncertainties; L₃ is extracted from these fits. For the unpolarized gas, we find ${L}_{3}^{0}=1.1(2)\times 1{0}^{-21}\,{{{{\rm{cm}}}}}^{6}/{{{\rm{s}}}}$. We estimate additional systematic uncertainties on L₃ of 20% due to box volume calibration (see “Methods”). b Normalized three-body loss coefficient ${L}_{3}/{L}_{3}^{0}$ at 690 G as a function of polarization, displayed on a ternary plot. c Histogram of L₃ in the unhatched region of (b). d Spin fraction and relative loss pairs (x_j, y_j) extracted from the decay of Fig. 2d; the error bars are the standard deviations of the time-resolved data and are often too small to be seen. The points lie on a line whose slope is η. e η at 690 G as a function of polarization on a ternary plot. Each point is an average over a single decay, as shown in (d); compared to (b) the points closest to the unpolarized case have been removed because η cannot be reliably extracted. The hatching marks two distinct regions in polarization space (see “Methods”). Histogram of η in the unhatched region of (e). f Top: (x_j, y_j) from the large (unhatched) region of the ternary plot in (e). The green solid line is a linear fit, η = 0.78(2). The gray dash-dotted line shows η = 0. Bottom: The same procedure at 845 G yields η = 0.02(3). We estimate an additional 5% systematic error on η (see “Methods”). The error bars are systematic error coming from slope determination.

We systematically extract L₃ from this total loss rate at 690 G as a function of polarization, see Fig. 3b-c. Unlike its spin-1/2 counterpart^47,48,49, the polarization of the three-component gas is characterized by two parameters. The spin fractions x_j ≡ n_j/n provide a convenient parameterization, so that the polarization state can be represented on a ternary plot. We find that over almost the entire region of the polarization space (unhatched region of Fig. 3b), the value of L₃ is largely independent of the spin composition, provided the spin fraction of $\left\vert 2\right\rangle$ is not very high (as seen in the histogram for ${L}_{3}/{L}_{3}^{0}$ in Fig. 3c; ${L}_{3}^{0}$ is the balanced-gas averaged value). Thus, from hereon, we fix ${L}_{3}={L}_{3}^{0}$ in our analysis.

With the total loss scaling established, we now investigate how losses are apportioned among the spins. Returning to Fig. 2d, we see that ΔN_j appears to be proportional to ${N}_{j}^{{{{\rm{initial}}}}}$. To characterize this relation, we introduce the relative losses ${y}_{j}\equiv {\dot{n}}_{j}/\dot{n}$ and compare them directly to the spin fractions x_j; we show in Fig. 3d the data extracted from Fig. 2d. This measurement suggests a simple relation:

$${y}_{j}=\eta {x}_{j}+\frac{1-\eta }{3},$$

(2)

where the proportionality of the losses is captured by the asymmetry η. The constant (1 − η)/3 is constrained by the definition of the parameters x_j and y_j; η = 0 corresponds to symmetric (normal) losses, as in Eq. (1).

Because x_j and y_j vary little during a typical decay at this field, we average over these values and produce a single value of η for a given decay (see Fig. S3 and Fig. S4 in Supplementary Information). Following this procedure, the ternary plot in Fig. 3e is populated with the values of η extracted from many different decays. We observe that the polarization space is separated into two regions of distinct behavior. In the (larger) region where $\left\vert 1\right\rangle$ or $\left\vert 3\right\rangle$ is the largest component (unhatched region in Fig. 3e), η is robust to spin composition, regardless of whether $\left\vert 2\right\rangle$ is the median or the minority component. In the (smaller) region where $\left\vert 2\right\rangle$ is the largest component (hatched in Fig. 3e), η is smaller, although distinctly non-zero. Note that exchanging spins $\left\vert 1\right\rangle$ and $\left\vert 3\right\rangle$ leaves Fig. 3e essentially unchanged, which reflects the approximate symmetry of the relevant scattering lengths (see Fig. 1b).

Gathering the data from the larger (unhatched) region, we observe that the law for the relative losses appears indeed to be universal over a large range of spin fractions. Fitting the data, we find η = 0.78(2) (see caption of Fig. 3f). On the other hand, applying the same procedure at B = 845 G, we find η = 0.02(3) (Fig. 3f), characteristic of the normal three-body loss dynamics of Eq. (1).

The behavior of both the total and relative losses suggests that the three-component mixture at 690 G obeys the following dynamics:

$${\dot{n}}_{j}=-3{L}_{3}\left(\eta {x}_{j}+\frac{1-\eta }{3}\right)\,{n}_{1}{n}_{2}{n}_{3}.$$

(3)

In Fig. 2d, we show as solid lines the solution of Eq. (3) with fixed L₃ ($={L}_{3}^{0}$) and η (= 0.78), using only the initial n_j as adjustable parameters; the agreement with the experimental data is excellent.

The form of Eq. (3) is reminiscent of a so-called avalanche mechanism, a debated topic in ultracold few-body dynamics^{50,51,52,53,54,55}. In an avalanche scenario, secondary collisions occur between the products of three-body recombination and other atoms in the gas, resulting in excess losses that augment the loss rate prefactor with spin-fraction-dependent terms. More specifically, the number of excess particles of spin $\left\vert \, j\right\rangle$ lost should be proportional to the fraction of atoms in that spin state, i.e., equal to cx_j. The prefactor c should be independent of the spin state to ensure that an unpolarized gas remains unpolarized during decay; c is then the average number of excess particles per recombination event. In this model, $\dot{n}\propto -(3+c){n}_{1}{n}_{2}{n}_{3}$ and thus η = c/(3 + c); our largest measured η would imply c ≳ 12. However, a generic kinetic model⁵¹ indicates that c ≲ 4 given the binding energies of the Feshbach dimers $\left\vert 12\right\rangle$ and $\left\vert 23\right\rangle$ (see section II in Supplementary Information).

This argument can be further strengthened. The likelihood of an avalanche strongly depends on the mean free path ℓ of the high-energy particles as they escape the trap. Given the elastic collision cross section σ = 4π/(k² + a⁻²), where k is the relative wavevector, the mean free path is ℓ = 1/(nσ) for escaping Feshbach dimers at a given density. Collecting additional decay measurements across a large density range, we observe that even though η slowly decreases at lower densities (Fig. 4a), it is still largely above zero even in the lowest density bin of Fig. 4a, for which ℓ ~ 200 μm is larger than the box (see “Methods”). Note that the variation of η is weak enough that it is negligible over our typical decay time series.

Fig. 4: Addressing candidate explanations for the loss anomaly.

a Asymmetry η versus total density n at 690 G. The points are obtained by gathering data from 23 decays into density bins and extracting the mean η from each decay. The highest two bins correspond to the data of Fig. 3e; this plot includes additional data at lower density. The variation of η with n is weak enough that it can be neglected over the density range considered during a typical decay (see “Methods”). b Loss coefficient L₃ versus η. The data bins are the same as in (a). L₃ is normalized to the unpolarized gas value ${L}_{3}^{0}=1.1\times 1{0}^{-21}\,{{{{\rm{cm}}}}}^{6}/{{{\rm{s}}}}$. The prediction from the avalanche model (see Supplementary Information) is shown as the purple line (with an arbitrary scaling factor for comparison with the experimental data). Error bars are standard deviations within bins. Inset: A cartoon depicting an avalanche process. After an initial inelastic scattering event, additional “spectator” particles are kicked out of the trap. c Fitted L₃ versus trap depth U. L₃ is normalized to the unpolarized gas measurement ${L}_{3}^{0}$, and U is normalized to the maximum box depth U_box = k_B × 1.6 μK. The error bars are the systematic error coming from L₃ determination. Inset: A cartoon depicting losses by evaporation. Energy released by inelastic processes could lead to losses via subsequent evaporation.

An avalanche process is also expected to lead to a relationship between L₃ and η, as a larger asymmetry would imply that more particles are involved in the avalanche and would therefore result in a higher effective loss rate. Indeed, in the model above, one finds ${L}_{3}\propto \frac{1}{1-\eta }$ (purple line in Fig. 4b, see Supplementary Information). Our data (blue points) is incompatible with such a relation.

Alternatively, three-body processes could deposit energy, leading to losses via subsequent evaporation; in the polarized gas, this could give rise to asymmetric losses, as suggested by ref. ⁵⁶. However, if the dominant loss process is evaporation, then L₃ should depend on the trap depth. We test this hypothesis by preparing an unpolarized gas at 20% of the full trap depth U_box. We let the gas settle in this shallow box for 500 ms. We then increase the trap depth to U and measure L₃ from the subsequent decay. As shown in Fig. 4c, we find that L₃ tends to a constant value ($\approx {L}_{3}^{0}$) at high trap depth. In fact, for U/U_box between 0.5 and 1, L₃ varies by less than 10%, showing that for U > 0.5U_box, the dynamics seem to be governed by a trap-depth-insensitive process (see caption of Fig. 4c).

We conclude our study with five final remarks. First, higher-body losses are ruled out by the total-density loss scaling $\dot{n}\propto -{n}_{1}{n}_{2}{n}_{3}$ (see Fig. 3a). It is possible for a higher-body process to mimic a three-body process, for example, if a multi-stage process is rate-limited by a three-body stage. But this requires the formation of an intermediate bound state, whose binding energy is of the order of the trap depth; no such suitable state is currently known. Secondly, processes that would exchange atoms between spin populations in the box (which could mimic some of our observations) are ruled out as spin exchange processes involve energies about two orders of magnitude larger than our trap depth, so any spin exchange process would result in direct atom loss. Third, the dynamics do not depend on the details of the spin-mixture preparation: changing the initial two-component mixture and the sequence of RF pulses do not affect the results (see “Methods”). Fourth, the effect is not specific to homogeneous gases: we indeed qualitatively observed the effect in harmonically trapped gases as well (although the uniform trap greatly simplifies the quantitative analysis); this also rules out that the anomaly could be caused by the blue-detuned box-trap light or the sharp box boundaries. Finally, we observed a nearly identical loss asymmetry at a nearby field (B = 705 G), showing that this effect is not exclusively present at the $\left\vert 1\right\rangle$-$\left\vert 3\right\rangle$ Feshbach resonance.

In summary, our observations of the anomalous decay are as follows. (I) In spin-balanced gases, losses appear largely symmetric, i.e., unpolarized gases remain unpolarized as they decay. (II) The process scales as three-body recombination involving all three spin components. (III) The total loss rate in a polarized gas is the same as in the unpolarized case. (IV) The relative loss of a given spin state is approximately linear in its spin fraction. (V) Neither quantum correlations, nor multiple scattering processes, nor higher-order loss terms appear to explain this behavior.

Future work should elucidate this puzzle, for example, by measuring the energy dynamics and temperature dependence of this process, as well as by characterizing the asymmetry across interaction regimes and monitoring for the anomalous formation of any intermediate states in the trap, such as dimers. This work also opens several new avenues, such as studying prethermalization dynamics of the metastable mixture^5,57 and searching for signatures of three-component pairing correlations at low temperature^25,26,27.

Note: During manuscript preparation, a theoretical study [arXiv:2509.06946] attributed the anomalous dynamics to secondary collisions and evaporative loss following three-body recombination. The theory predicts large asymmetric loss even in unpolarized samples—contrary to experiment—and bound states proposed to cause the secondary collisions were absent in a calibrated RF spectroscopy measurement.

Methods

Characterizing optical boxes

We determine the volume of the optical box of Fig. 1 of the main text by fitting the in situ density profiles ∫dz n_j(x, y, z) (where z is the imaging line of sight) with a conical frustum model of radii R₁ and R₂, and length L, convolved with a Gaussian function of standard deviations σ_x and σ_y (that capture imperfections from finite resolution of the imaging and box projection systems). We find R₁ = 75(1) μm, R₂ = 73(1) μm, L = 120(2) μm. The values of σ_x = 2.4 μm and σ_y = 3.8 μm reflect the slightly different quality of projection of the “end caps" and the “tube" of the box. In Fig. 5b, we display density profile cuts of the box of Fig. 1c of the main text projected along the x and y axes together with the fits (dashed purple lines).

Fig. 5: Homogeneity of a polarized three-component mixture in the optical box.

a Example of an in situ optical density image of $\left\vert 3\right\rangle$ (same data as Fig. 1c with x₁ = 0.16, x₂ = 0.35, and x₃ = 0.49). b Cuts of the density profile (yellow, solid) and the fit (purple, dashed) along the y (top) and x (bottom) axes (dashed black lines in (a)). The fit to the OD image is a smoothed cone (see text). Residuals (normalized to the peak fitted density along each cut) are shown underneath. c Top: Subtracting the measured in situ density of $\left\vert 3\right\rangle$ from $\left\vert 2\right\rangle$ (after scaling $\left\vert 2\right\rangle$ to have the same mean density as $\left\vert 3\right\rangle$). OD scale is the same as (a), and the dashed red rectangle indicates the region of the box. Bottom: Likewise, subtracting spin $\left\vert 3\right\rangle$ from $\left\vert 1\right\rangle$.

If imperfections were entirely due to the box projection system—a conservative assumption—we estimate that  ≈ 90% of the atoms are within 10% of the average density in the box. Additionally, we observe during a typical decay that the volume decreases by  ≈ 10% when the atom number decreases by a factor of  ≈ 5; taking this small effect into account as an uncertainty on the volume, we estimate an uncertainty of 10% on γ and of 20% on L₃. This also contributes to uncertainties on x_j, y_j of  ≈ 1% and  ≈ 5% respectively (reflecting the difference between fitting N and $\dot{N}$ rather than n and $\dot{n}$). Ultimately, we find that the uncertainty in η due to this effect is  ≈ 5%.

The three spin components are levitated against gravity using a magnetic field gradient. For B ≥ 690 G, the relative difference in magnetic moments between the spins is less than h × 10 kHz/G (h is Planck’s constant). Assuming that $\left\vert 1\right\rangle$ is magnetically levitated against gravity (∣dB/dy∣ ≈ 1 G/cm), the residual forces on $\left\vert 2\right\rangle$ and $\left\vert 3\right\rangle$ are less than 1% of gravity, corresponding to an energy less than k_B × 5 nK over the length scale of our box, which is small compared to both our E_F and T. In Fig. 5c, we compare the density profiles of the three spin states by scaling and subtracting the profiles from each other. We see that the density profiles are essentially identical up to rescaling.

Two- and three-component decay versus magnetic field

In this section, we show that in the range of B explored in this work, unpolarized three-component mixtures decay much faster than any two-component ones; furthermore, the power law of the decay is measured as a function of B.

In Fig. 6a, we show examples of decays of two-component mixtures (which may include evaporative losses in addition to intrinsic recombination processes). We compare two- and three-component decays quantitatively in Fig. 6b by extracting an (early-time) effective timescale for losses ${\tau }_{{{{\rm{eff}}}}}=n/| \dot{n}|$. The black crosses correspond to three-component mixtures, with a density per spin state in the range n_j ≈ (1.5 − 4) × 10¹¹ cm⁻³. In green, blue and pink, we show τ_eff for the two-component mixtures; for each field, the density per spin state is up to a factor of 4 larger than the corresponding three-component data, but never smaller. Even in that case, τ_eff is at least an order of magnitude larger than the corresponding three-component one.

Fig. 6: Stability of two- versus three-component mixtures.

a Decay of unpolarized two-component gases at 690 G; a three-component gas decay is shown as black crosses for reference. b Effective timescales ${\tau }_{{{{\rm{eff}}}}}=n/| \dot{n}|$ of two and three-component samples across magnetic fields. Feshbach resonances are indicated by vertical dash-dotted lines. At each field shown, the two-component gases have densities (per spin state) equal to or greater than those of the corresponding three-component gas. Solid pink and blue curves show predictions from universal recombination to Feshbach dimers^40,58. For B larger than the red dotted line, the $\left\vert 12\right\rangle$ and $\left\vert 23\right\rangle$ Feshbach dimers can remain trapped. The error bars in both (a) and (b) are the standard deviations of three measurements and are smaller than the marker size. c L₃ versus polarization at 690 G (normalized to ${L}_{3}^{0}$ as in the main text), includes additional data at lower total density (n ~ 5 × 10¹⁰ cm⁻³) not shown in the main text. The dashed red curve gives polarization outside which two-component processes are expected to account for 10% of total losses or more.

However, this will no longer hold for extremely polarized three-component gases. At B = 690 G, both a₁₂ and a₂₃ are positive so that the corresponding two-component mixtures are already unstable with respect to three-body recombination (involving two identical fermions⁵⁸). Furthermore, the corresponding binding energies of the $\left\vert 12\right\rangle$ and $\left\vert 23\right\rangle$ dimers are such that all recombination products escape from the box (see section II in Supplementary Information). Thus, a mixture of spins $\left\vert i\right\rangle$-$\left\vert \, j\right\rangle$ would decay following a recombination law ${\dot{n}}_{j}=-{L}_{3}^{ij}(2{n}_{j}^{2}{n}_{i}+{n}_{i}^{2}{n}_{j})/3$. We note that the two-component recombination rates agree with the universal prediction of ref. ⁵⁸ (solid lines of Fig. 6b) at fields below 720 G (red dotted line of Fig. 6b). At higher magnetic fields, the formation of $\left\vert 12\right\rangle$ and $\left\vert 23\right\rangle$ dimers does not directly lead to losses, as their binding energies are less than 6U_box (ref. ⁴⁰).

To estimate the influence of two-component losses on the main text’s analysis, we calculate the ratio of the total losses due to three-component recombination (${\dot{n}}_{{{{\rm{three}}}}}\equiv -3{L}_{3}{n}_{1}{n}_{2}{n}_{3}$) to two-component ones (${\dot{n}}_{{{{\rm{two}}}}}\equiv -{L}_{3}^{12}({n}_{1}^{2}{n}_{2}+{n}_{2}^{2}{n}_{1})-{L}_{3}^{23}({n}_{2}^{2}{n}_{3}+{n}_{3}^{2}{n}_{2})$):

$$\frac{{\dot{n}}_{{{{\rm{two}}}}}}{{\dot{n}}_{{{{\rm{three}}}}}}=\frac{{L}_{3}^{12}}{3{L}_{3}}\left(1/{x}_{3}-1\right)+\frac{{L}_{3}^{23}}{3{L}_{3}}\left(1/{x}_{1}-1\right).$$

(4)

Extracting ${L}_{3}^{12}$ and ${L}_{3}^{23}$ from Fig. 6a, we find ratios ${L}_{3}^{12}/(3{L}_{3}) < 0.003$ and ${L}_{3}^{23}/(3{L}_{3}) < 0.001$ at 690 G. Setting a limit of ${\dot{n}}_{{{{\rm{two}}}}}/{\dot{n}}_{{{{\rm{three}}}}} < 10\%$, we find the polarization limit depicted as red dashed lines in Fig. 6c. For mixtures less polarized than this limit (which includes almost all of our data), three-component losses are dominant, and we ignore losses arising from two-component processes.

We also note that our measured three-component recombination rate ${L}_{3}^{0}$ at 690 G is similar to an unpolarized-gas measurement in a harmonic trap at a nearby field³⁴, but significantly smaller than a theoretical prediction⁴⁴ (however, unitary saturation due to finite temperature effects could suppress the predicted resonant enhancement). Our measurements of L₃ above 800 G are similar to the values reported in ref. ³⁵.

The fact that the dominant loss mechanism involves all three components does not imply that the loss behavior is necessarily three-body like. To address this question, we measure the decays of unpolarized three-component mixtures and extract the power law scaling $\dot{n}\propto -{n}^{\gamma }$, see Fig. 7. At low (B ≲ 720 G) and high (B ≳ 810 G) fields, γ ≈ 3 and the losses are three-body dominated. The intermediate range is more complicated, and γ deviates from 3. In that region, the scattering lengths a₁₂ and a₂₃ are large and positive, so that the products of three-body recombination can remain trapped^40,58. This allows for subsequent inelastic atom-dimer collisions (involving three distinguishable atoms), which is an effectively two-body loss process^44,59,60,61. Our intermediate 2 ≲ γ ≲ 3 is qualitatively consistent with this competition of two- and three-body effects.

Fig. 7: Three-component decay versus magnetic field B.

Exponent γ characterizing the power-law decay ($\dot{n}\propto -{n}^{\gamma }$). The Feshbach resonances are shown as dot-dashed gray lines. For B larger than the red dotted line, the $\left\vert 12\right\rangle$ and $\left\vert 23\right\rangle$ Feshbach dimers largely remain trapped after formation (see text). Error bars on γ displayed are only statistical (estimated by bootstrapping). For most points, the dominant source of uncertainty is an additional 10% systematic error coming from box volume calibration.

For the sake of simplicity, we avoid this intermediate regime in the study presented in the main text. A measurement at 705 G yields η = 0.8(1), showing that the asymmetric losses do not only occur at the $\left\vert 1\right\rangle$-$\left\vert 3\right\rangle$ resonance.

Spin fraction dynamics

Here we show that under the effective decay Eq. (3) in the main text, the two distinct regions of polarization in the ternary plot Fig. 3e are closed under time evolution, i.e., time dynamics does not allow for crossing from the hatched area into the unhatched one (and vice-versa). Indeed, Eq. (3) implies

$$\dot{{{{\bf{x}}}}}=(1-\eta )\frac{3{L}_{3}{n}_{1}{n}_{2}{n}_{3}}{{n}_{1}+{n}_{2}+{n}_{3}}\left({{{\bf{x}}}}-{{{\bf{c}}}}\right),$$

(5)

where x = (x₁, x₂, x₃) and ${{{\bf{c}}}}=\frac{1}{3}(1,1,1)$. The spin fraction flow is a ray from the unpolarized state c, shown in Fig. 8a.

Fig. 8: Spin fraction dynamics under asymmetric three-body decay.

a Map of the polarization flow following Methods Eq. (5). b Examples of polarization dynamics at B = 690 G (top) and B = 845 G (bottom) from Fig. 2b, d of the main text. Empty points are neglected, owing to early-time effects. The solid lines are solutions to Eq. (5).

In Fig. 8b, we show the spin fractions over time, with the predictions of Eq. (5) (solid lines). We note that the magnitude $| \dot{{{{\bf{x}}}}}|$, the “speed" of this flow, is suppressed for large η. Indeed, at B = 690 G the spin fractions barely change, while at B = 845 G, they vary significantly.

This polarization flow has an interesting consequence: if η is large, a two-component gas with a small contaminant of a third state will purify into a two-component mixture at a large cost in particle loss. Indeed, considering a nearly balanced mixture $\left\vert 1\right\rangle$-$\left\vert 3\right\rangle$ with a contaminant of $\left\vert 2\right\rangle$, x₂ ≪ x₁ = x₃, the loss rate ratio is

$$\frac{{\dot{n}}_{1}+{\dot{n}}_{3}}{{\dot{n}}_{2}}=\frac{2+\eta (1-3{x}_{2})}{1-\eta (1-3{x}_{2})}.$$

(6)

This ratio approaches 14 for η = 0.8 as x₂ → 0. However, measuring three-component losses in the extremely polarized limit x₂ → 0 is challenging, as the three-body loss timescale (n₁ + n₂ + n₃)/(L₃n₁n₂n₃) becomes larger and other effects, such as the trap lifetime and residual evaporation, become important. For the highly polarized decay of Fig. 9, the three-body losses remain dominant and follow the model presented in the main text. In the regime 0.02 < x₂ < 0.10, we verify that $({\dot{n}}_{1}+{\dot{n}}_{3})/{\dot{n}}_{2}\approx 8$, in good agreement with Eq. (6) (red points in Fig. 9a).

Fig. 9: Decay dynamics of a highly polarized gas.

a Decay of a gas where $\left\vert 2\right\rangle$ is an impurity, and the initial fraction is x₂ ≈ 0.1. Solid lines are fits where L₃ is fixed to ${L}_{3}^{0}$ and η = 0.78. The error bars are the standard deviations of three measurements and are smaller than the marker size. Inset: $-\dot{n}$ versus n₁n₂n₃. The upper dashed line marks the early-time slow decay. The lower dashed line marks x₂ = 0.02. The red band corresponds to ${L}_{3}^{0}{n}_{1}{n}_{2}{n}_{3}$ including the uncertainty on ${L}_{3}^{0}$. b y_j versus x_j from every red point in the inset of (a); the black solid line corresponds to η = 0.78. The error bars are systematic error coming from slope determination.

RF preparation protocols

Here, we provide further details on the RF preparation of the three-component mixtures. To cover extensively the polarization space, we used several RF protocols and different initial spin mixtures, as depicted in Fig. 10. The ternary plot is populated with the data of Fig. 3e, with symbols corresponding to the protocol used. Depending on the initial spin states used, the initial evaporation of the two-component mixture was carried out at different magnetic fields B₀ as noted in Fig. 10. We see that the different protocols produce consistent values in the regions where they overlap, implying that the results do not depend on the details of the RF preparation. Since the protocols start with various incoherent two-component mixtures, this also indicates that RF coherence is unlikely to play a role in the (long-time) anomalous dynamics.

Fig. 10: Robustness of η with respect to RF preparation protocols.

Data from Fig. 3e, where symbols in the ternary plot now correspond to the RF preparation protocols (see left cartoons and legend). Colored circles indicate initial and final spin populations, and arrows denote the RF pulses. B₀ is the magnetic field at which the two-component gas was evaporated (prior to the RF pulses).

A simple loss model on a lattice

In this section, we show that a generic model does not account for the loss asymmetry. We consider a model of a gas on a three-dimensional lattice of lattice spacing b. Treating the gas as an open quantum system, we calculate the rate of change of atom number $\frac{{{{\rm{d}}}}}{{{{\rm{d}}}}t}\left\langle {N}_{j}\right\rangle={{{\rm{tr}}}}\left(\dot{\rho }{N}_{j}\right)$ using the Lindblad equation^62,63:

$$\dot{\rho }=\frac{1}{i\hslash }\left[{H}_{{{{\rm{sys}}}}},\rho \right]+{\sum}_{\alpha }\left({L}_{\alpha }\rho {L}_{\alpha }^{{{\dagger}} }-1/2\,\{{L}_{\alpha }^{{{\dagger}} }{L}_{\alpha },\rho \}\right),$$

(7)

where ρ is the density matrix of the system, and H_sys is the system’s (conservative) Hamiltonian, containing the kinetic, potential and elastic interaction energies. The atom number operator N_j in state $\left\vert \, j\right\rangle$ is defined as ${N}_{j}={\sum}_{\alpha }{b}^{3}{a}_{j,\alpha }^{{{\dagger}} }{a}_{j,\alpha }$, where the operators a_j,α and ${a}_{j,\alpha }^{{{\dagger}} }$ respectively annihilate and create a particle of spin $\left\vert \, j\right\rangle$ at lattice site α (in this section only, N_j is defined as an operator. In the rest of the text, it is an average value). These operators satisfy the anti-commutation relations: {a_i,α, a_j,β} = 0 and $\{{a}_{i,\alpha },{a}_{j,\beta }^{{{\dagger}} }\}={\delta }_{i,j}{\delta }_{\alpha,\beta }/{b}^{3}$. ${L}_{\alpha }=\sqrt{\kappa }{a}_{1,\alpha }{a}_{2,\alpha }{a}_{3,\alpha }$ is the non-hermitian jump operator which represents the inelastic process: three particles of different spin states scatter inelastically with a probability ∝ κ when they are located on the same lattice site α, causing them to escape the trap. This yields

$$\frac{{{{\rm{d}}}}}{{{{\rm{d}}}}t}\left\langle {N}_{j}\right\rangle=\sum\limits_{\alpha,\beta }\left\langle {L}_{\alpha }^{{{\dagger}} }({b}^{3}{a}_{j,\beta }^{{{\dagger}} }{a}_{j,\beta }){L}_{\alpha }-1/2\{{L}_{\alpha }^{{{\dagger}} }{L}_{\alpha },{b}^{3}{a}_{j,\beta }^{{{\dagger}} }{a}_{j,\beta }\}\right\rangle,$$

(8)

Since we have observed no spin-changing collisions in any two-component mixture, we have assumed that H_sys commutes with all N_j. Using $\left\langle {L}_{\alpha }^{{{\dagger}} }({b}^{3}{a}_{j,\beta }^{{{\dagger}} }{a}_{j,\beta }){L}_{\alpha }\right\rangle=\left\langle {L}_{\alpha }^{{{\dagger}} }{L}_{\alpha }({b}^{3}{a}_{j,\beta }^{{{\dagger}} }{a}_{j,\beta })\right\rangle -{\delta }_{\alpha,\beta }\left\langle {L}_{\alpha }^{{{\dagger}} }{L}_{\alpha }\right\rangle$ and $\left\langle \{{L}_{\alpha }^{{{\dagger}} }{L}_{\alpha },({b}^{3}{a}_{j,\beta }^{{{\dagger}} }{a}_{j,\beta })\}\right\rangle=2\left\langle {L}_{\alpha }^{{{\dagger}} }{L}_{\alpha }({b}^{3}{a}_{j,\beta }^{{{\dagger}} }{a}_{j,\beta })\right\rangle$, we simplify Eq. (8) into⁴⁶

$$\frac{{{{\rm{d}}}}}{{{{\rm{d}}}}t}\left\langle {N}_{j}\right\rangle=-\sum\limits_{\alpha }\left\langle {L}_{\alpha }^{{{\dagger}} }{L}_{\alpha }\right\rangle=-\kappa \sum\limits_{\alpha }\left\langle {a}_{3,\alpha }^{{{\dagger}} }{a}_{2,\alpha }^{{{\dagger}} }{a}_{1,\alpha }^{{{\dagger}} }{a}_{1,\alpha }{a}_{2,\alpha }{a}_{3,\alpha }\right\rangle .$$

(9)

There is thus no dependence on the spin label j, and each spin component shares the losses equally: η = 0.

Mean free path

Avalanche processes require high collisional opacity of the product states in the medium. However, we measure significant asymmetry even at low densities where the mean free path of typical recombination products ℓ exceeds the system size.

For s-wave scattering of distinguishable particles, the collision cross section is σ = 4π/(k² + a⁻²), where a is the relevant scattering length and $k=\sqrt{2\mu E}/\hslash$ is the relative wavevector for a reduced mass μ and energy E. For a typical dimer $\left\vert 12\right\rangle$ and free atom $\left\vert 3\right\rangle$ formed after recombination, k ≈ 1 × 10⁷ m⁻¹. The dimer (which scatters off all spin states) has the shorter mean free path:

$$\ell \approx {\left({n}_{1}{\sigma }_{1}+{n}_{2}{\sigma }_{2}+{n}_{3}{\sigma }_{3}\right)}^{-1} \sim 200\,\mu {{{\rm{m}}}},$$

(10)

where we have used n₁ = n₂ = n₃ = 2 × 10¹⁰ cm⁻³ (corresponding to the lowest density bin of Fig. 4a of the main text), and σ_j is the collisional cross section between the free atom $\left\vert \, j\right\rangle$ and the dimer $\left\vert 12\right\rangle$. For this density, even a single secondary scattering following an inelastic collision is thus not very likely in a box of size  ~ 150 μm. Yet, even in those conditions, we observe a large η ≳ 0.5. The result is similar for the process involving a typical $\left\vert 23\right\rangle$ dimer and one atom.

We repeated the experiment in a smaller, near-cubical box of size  ≈ 30 μm. In that box, a random particle would travel an average distance of 14 μm (in the absence of collisions) before reaching the box boundary. Given an initial total density n ≈ 7 × 10¹¹ cm⁻³, ℓ > 21 μm during the entire decay. Even in that case, we find η = 0.8(1), consistent with the measurements of the main text. We conclude that an avalanche process is an unlikely explanation.

We note that in these calculations, we have assumed that particles that reach the trap boundary are lost. We have ignored the effect of “glancing” collisions, where particles with energy greater than the trap depth can be confined if they have a sufficiently shallow angle of incidence with the trap walls. In this case, the effective travel length is increased. Estimating this effect depends sensitively on the trap potential and geometry as well as the distribution of product energies. However, the fact that the observed loss rate does not depend strongly on the trap depth (see Fig. 4c of the main text) suggests that this effect does not contribute to our observations. To further rule out the role of this effect, we also performed polarized decay measurements in other trap shapes, including traps with Sinai billiard and Bunimovich stadium cross-section (which are notoriously ergodic). The resulting η values are consistent with those reported in the main text at comparable densities, suggesting that the trapping geometry does not significantly affect the asymmetric loss.