Coherent States in Quantum Systems
Summary
Coherent states constitute a class of quantum states that most closely resemble the behaviour of classical oscillators while fully respecting quantum uncertainty principles. Originally introduced in the context of the quantum harmonic oscillator, they were later generalised via group-theoretic constructions to encompass a wide variety of physical systems. Characterised by minimal uncertainty and a well-defined phase-space representation, coherent states are generated by the action of displacement or symmetry operators on a reference vacuum or extremal state. Their overcomplete basis structure enables efficient decompositions of arbitrary quantum states and underpins modern techniques in quantum optics, information processing, metrology and condensed-matter simulations. Extensions to non-harmonic potentials and interacting systems have fostered the development of nonlinear coherent states and variational families tailored to many-body dynamics, while phase-space formulations have provided deep geometric insights into quantum evolution and control.
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Coherent States in Quantum Systems publication trend
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Technical terms
Coherent state: A quantum state obtained by displacing or applying group operations to a reference state, minimising uncertainty and admitting a quasi-classical phase-space description.
Gaussian state: A state whose Wigner or characteristic function is Gaussian, fully specified by first and second moments of canonical operators, often used in bosonic and fermionic systems.
Ladder operator: An operator that raises or lowers the eigenvalue of a given Hamiltonian’s eigenstate, fundamental to the algebraic construction of coherent states.
Variational method: A computational strategy that approximates quantum dynamics or ground states by optimising parameters of a chosen trial wavefunction or state manifold.
Kähler structure: A geometric framework combining symplectic and complex structures on a manifold, used to characterise families of Gaussian states and their dynamics.
References
- Generalization of group-theoretic coherent states for variational calculations. Physical Review Research (2021).
- Bosonic and fermionic Gaussian states from Kähler structures. SciPost Physics Core (2021).
- Local optimization on pure Gaussian state manifolds. SciPost Physics (2021).
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