Quantum catastrophes and ergodicity in the dynamics of bosonic Josephson junctions

Abstract

We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory the rainbows are singular caustics, but in the second-quantized theory a Poisson resummation of the wave function shows that they are described by well behaved Airy functions. The structural stability of these Fock space caustics against variations in the initial conditions and Hamiltonian evolution is guaranteed by catastrophe theory. We also show that the long-time dynamics are ergodic. Our results are relevant to the question posed by Berry [M.V. Berry, Nonlinearity 21, T19 (2008)]: are there circumstances when it is necessary to second-quantize wave theory in order to avoid singularities?

5 pages, 3 figures. New references added plus a section on experimental realizability

References in corpus (12)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Thermalization and its mechanism for generic isolated quantum systems
• Nonlinear atom interferometer surpasses classical precision limit
• Squeezing and entanglement in a Bose-Einstein condensate
• Alternatives to Eigenstate Thermalization
• Preparing and probing atomic number states with an atom interferometer
• Dynamics of a tunable superfluid junction
• Many-body Landau-Zener dynamics in coupled 1D Bose liquids
• Commutability between Semiclassical Limit and Adiabatic Limit
• Semiclassical quantization of an N-particle Bose-Hubbard model
• Josephson effect and quantum merging of two Bose superfluids
• Caustic formation in expanding condensates of cold atoms

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• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
• Quantum spin dynamics in Fock space following quenches: Caustics and vortices
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Exactly solvable model behind Bose-Hubbard dimers, Ince-Gauss beams, and aberrated optical cavities
• Dissipative Bose-Josephson junction coupled to bosonic baths
• Emergence of singularities from decoherence: Quantum catastrophes
• Gravitational Caustics in an Atom Laser
• Displaced harmonic oscillator $V\sim \min [(x+d{)}^2,(x-d{)}^2]$ as a benchmark double-well quantum model
• Polynomial potentials and coupled quantum dots in two and three dimensions
• Arnold's potentials and quantum catastrophes II
• Atom Interferometric Imaging of Differential Potentials Using an Atom Laser
• Dynamical Phase Transitions, Caustics, and Quantum Dark Bands
• Caustics in the sine-Gordon model from quenches in coupled 1D Bose gases
• Emergence of caustics in dynamics of the Kitaev model