Figure 1
From: Realizing and characterizing chiral photon flow in a circuit quantum electrodynamics necklace
(a) Schematic plot of the SQUID-coupled three-TLR necklace. This circuit is constructed by three TLRs connected through the grounding SQUIDs. For each SQUID α, the SQUID loop is penetrated by a static bias flux 
and a dynamic modulation pulse δΦα with α = a, b, c. Moreover, each TLR is coupled to a measurement device which can detect its photon number. The lowest three eigenfrequencies of the circuit are labeled by ω1, ω2 and ω3, respectively. (b), (c) The localization property of the eigenmodes. (c) depicts the normalized mode functions of the three lowest eigenmodes of the circuit QED necklace versus critical currents of the SQUIDs. The three panels of (c) describe the eigenmode functions corresponding to the eigenmode 1, 2 and 3 respectively. The blue solid line, green dash line and red dot-dashed line correspond to the situations of IS = Ia = Ib = Ic = 1, 2, 3 μA respectively. In addition, we set EJα/ECα = 100 with ECα = 2e2/CJα. With the chosen parameters, we get ω1/2π = 11.5 GHz, ω2/2π = 9.5 GHz and ω3/2π = 8.2 GHz for IS = 3 μA. In (b), we quantify the localization property of the mth eigenmode by Em/ωm where Em is the energy stored in the mth TLR for m = 1, 2, 3. The critical current IS of the SQUIDs varies from 0.5 μA to 4 μA and the other parameters are chosen as the same as in Fig. 1(c). (d) Square lattice consisting of four kinds of TLRs. Four kinds of TLRs with different eigenfrequencies (red for ω1/2π = 8 GHz, orange for ω2/2π = 9 GHz, blue for ω3/2π = 10 GHz and dark blue for ω4/2π = 11 GHz) are placed in an interlaced form and coupled by grounding SQUIDs. With proper pumping pulses, only nearest-neighbor parametric photon hopping can be induced.
