Dynamical Phase Transitions, Caustics, and Quantum Dark Bands

Abstract

We provide a new perspective on quantum dynamical phase transitions (DPTs) by explaining their origin in terms of caustics that form in the Fock space representation of the many-body state over time, using the fully connected transverse field Ising model as an example. In this way we establish a connection between DPTs in a quantum spin system and an everyday natural phenomenon: The dark band between the primary and seconday bows (caustics) in rainbows known as Alexander's dark band. The DPT occurs when the Loschmidt echo crosses the switching line between the evanescent tails of two back-to-back Airy functions that dress neighbouring fold caustics in Fock space and is the time-dependent analogue of what is seen as a function of angle in the sky. The structural stability and universal properties of caustics, as described mathematically by catastrophe theory, explains the generic occurrence of DPTs in the model and suggests that our analysis has wide applicability. Based on our thorough analytical understanding we propose a protocol which can be used to verify the existence of a DPT in a finite system experiment.

References in corpus (78)

• Nonequilibrium dynamics of closed interacting quantum systems
• The large deviation approach to statistical mechanics
• Many-body localization, thermalization, and entanglement
• Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
• Continuous Quantum Phase Transitions
• Quantum many-body systems out of equilibrium
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Observation of entanglement propagation in a quantum many-body system
• Josephson Junction Arrays with Bose-Einstein Condensates
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Classical bifurcation at the transition from Rabi to Josephson dynamics
• Observation of a dynamical topological phase transition
• Dynamical phase transition in the open Dicke model
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Macroscopic quantum self-trapping and Josephson oscillations of exciton-polaritons
• Excited state quantum phase transitions in many-body systems
• Coherent Oscillations in an Exciton-Polariton Josephson Junction
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Dynamical phase transitions after quenches in non-integrable models
• Observation of universal dynamics in a spinor Bose gas far from equilibrium
• Freak waves in the linear regime: A microwave study
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Observation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium
• Exploring dynamical phase transitions with cold atoms in an optical cavity
• Universal Prethermal Dynamics of Bose Gases Quenched to Unitarity
• Dynamics of a tunable superfluid junction
• Excited-State Quantum Phase Transitions in Dicke Superradiance Models
• Ergodicity and large deviations in physical systems with stochastic dynamics
• Observation of Quantum Phase Transitions with Parity-Symmetry Breaking and Hysteresis
• Excited-state quantum phase transitions
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases
• Dynamical Quantum Phase Transitions: A Geometric Picture
• Observable and hidden singular features of large fluctuations in nonequilibrium systems
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Dynamic scaling of fronts in the quantum XX chain
• Non-equilibrium dynamics of an unstable quantum pendulum
• Dynamical critical scaling of long-range interacting quantum magnets
• Dynamical quantum phase transitions: a brief survey
• Dynamical phase transition in large deviation statistics of the Kardar-Parisi-Zhang equation
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Statistics of Extreme Waves in Random Media
• Dynamical and excited-state quantum phase transitions in collective systems
• Hydrodynamical phase transition for domain-wall melting in the XY chain
• Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice
• Landau theory of the short-time dynamical phase transitions of the Kardar-Parisi-Zhang interface
• Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench
• Dynamical phase transitions in dissipative quantum dynamics with quantum optical realization
• Non-Markovian Quantum Dynamics in Strongly Coupled Multimode Cavities Conditioned on Continuous Measurement
• Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
• Dynamical quantum phase transitions in collapse and revival oscillations of a quenched superfluid
• Analytical results for Josephson dynamics of ultracold Bosons
• Anatomy of Dynamical Quantum Phase Transitions
• Quantum catastrophes and ergodicity in the dynamics of bosonic Josephson junctions
• WKB approach and quantum corrections to classical dynamics in the Josephson problem
• Demonstration of fold and cusp catastrophes in an atomic cloud reflected from an optical barrier in the presence of gravity
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain
• Time-dependent Semiclassics for Ultracold Bosons
• Quantum caustics and the hierarchy of light cones in quenched spin chains
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions
• Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
• Quantum spin dynamics in Fock space following quenches: Caustics and vortices
• Mechanism of dynamical phase transitions: The complex-time survival amplitude
• Exactly solvable model behind Bose-Hubbard dimers, Ince-Gauss beams, and aberrated optical cavities
• Emergence of singularities from decoherence: Quantum catastrophes
• Limit shape phase transitions: a merger of arctic circles
• Gravitational Caustics in an Atom Laser
• Scaling at the OTOC Wavefront: free versus chaotic models
• Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions