Quantum phase space picture of Bose-Einstein Condensates in a double well: Proposals for creating macroscopic quantum superposition states and a study of quantum chaos

Abstract

We present a quantum phase space model of Bose-Einstein condensate (BEC) in a double well potential. In a two-mode Fock-state analysis we examine the eigenvectors and eigenvalues and find that the energy correlation diagram indicates a transition from a delocalized to a fragmented regime. Phase space information is extracted from the stationary quantum states using the Husimi distribution function. It is shown that the quantum states are localized on the known classical phase space orbits of a nonrigid physical pendulum, and thus the novel phase space characteristics of a nonrigid physical pendulum such as the $\pi$ motions are seen to be a property of the exact quantum states. Low lying states are harmonic oscillator like libration states while the higher lying states are Schrödinger cat-like superpositions of two pendulum rotor states. To study the dynamics in phase space, a comparison is made between a displaced quantum wavepacket and the trajectories of a swarm of points in classical phase space. For a driven double well, it is shown that the classical chaotic dynamics is manifest in the dynamics of the quantum states pictured using the Husimi distribution. Phase space analogy also suggests that a $\pi$ phase displaced wavepacket put on the unstable fixed point on a separatrix will bifurcate to create a superposition of two pendulum rotor states - a Schrödinger cat state (number entangled state) for BEC. It is shown that the choice of initial barrier height and ramping, following a $\pi$ phase imprinting on the condensate, can be used to generate controlled entangled number states with tunable extremity and sharpness.

revised version, 13 pages, 13 figures

References in corpus (14)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Dark Solitons in Bose-Einstein Condensates
• Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
• Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
• Quantum Superposition States of Bose-Einstein Condensates
• Many particle entanglement in two-component Bose-Einstein Condensates
• Spatial fragmentation of a Bose-Einstein condensate in a double-well potential
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• States without linear counterpart in Bose-Einstein condensates
• Evolution of the macroscopically entangled states in optical lattices
• Bose-Einstein condensates in a one-dimensional double square well: Analytical solutions of the Nonlinear Schrödinger equation and tunneling splittings
• The dynamics of a strongly driven two component Bose-Einstein Condensate
• Phase engineering of controlled entangled number states in a single component Bose-Einstein condensate in a double well
• Macroscopic Quantum Coherence in a repulsive Bose-Einstein condensate

Cited by in corpus (101)

• The Gross-Pitaevskii Equation for Bose Particles in a Double Well Potential: Two Mode Models and Beyond
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Periodic Modulation Effect on Self-Trapping of Two weakly coupled Bose-Einstein Condensates
• Spontaneous symmetry breaking of solitons trapped in a double-channel potential
• Ultracold Bosons in a Tilted Multi-level Double-Well Potential
• Quantum Entanglement Manifestation of Transition to Nonlinear Self-trapping for Bose-Einstein Condensates in a Symmetric Double-Well
• Nonlinear quantum interferometry with Bose condensed atoms
• Quantum dynamics in the bosonic Josephson junction
• Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics
• Semiclassical approach to Bose-Einstein condensates in a triple well potential
• Nonlinear phase-dynamics in a driven Bosonic Josephson junction
• Semiclassical quantization of an N-particle Bose-Hubbard model
• Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials
• Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity
• Coherence and entanglement in the ground-state of a bosonic Josephson junction:from macroscopic Schrödinger cats to separable Fock states
• Dynamical Realization of Macroscopic Superposition States of Cold Bosons in a Tilted Double Well
• Optimal control of quantum superpositions in a bosonic Josephson junction
• Quantum dynamics of bosons in a double-well potential: Josephson oscillations, self-trapping and ultralong tunneling times
• Spontaneous symmetry breaking in Schrödinger lattices with two nonlinear sites
• Control of the Bose-Einstein condensate by dissipation. Nonlinear Zeno effect
• Scattering bright solitons: quantum versus mean-field behavior
• Nonlinear modes and symmetry breaking in rotating double-well potentials
• Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling
• Bose-Einstein Condensates on slightly asymmetric double-well potentials
• Multiconfigurational Hartree-Fock theory for identical bosons in a double well
• Optical realization of the two-site Bose-Hubbard model in waveguide lattices
• Tunneling, self-trapping and manipulation of higher modes of a BEC in a double well
• Two coupled nonlinear cavities in a driven-dissipative environment
• Analytical results for Josephson dynamics of ultracold Bosons
• Universality in nonadiabatic behaviour of classical actions in nonlinear models with separatrix crossings
• The driven-dissipative Bose-Hubbard dimer: phase diagram and chaos
• Relaxation, chaos, and thermalization in a three-mode model of a BEC
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Macroscopic Quantum Tunneling Escape of Bose-Einstein Condensates
• Chaos in the three-site Bose-Hubbard model -- classical vs quantum
• Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
• Efficient creation of maximally entangled states by modulation of tunneling rates
• Macroscopic Superposition of Ultracold Atoms with Orbital Degrees of Freedom
• NOON state of Bose atoms in the double-well potential via an excited state quantum phase transition
• Macroscopic superposition states of ultracold bosons in a double-well potential
• Quantum chaos in a Bose-Hubbard dimer with modulated tunnelling
• Nonlinear energy transfer in classical and quantum systems
• Global Phase Space of Coherence and Entanglement in a double-well BEC
• Floquet analysis of the modulated two-mode Bose-Hubbard model
• NOON states with ultracold bosonic atoms via resonance- and chaos-assisted tunneling
• Change in the adiabatic invariant in a nonlinear two-mode model of Feshbach resonance passage
• Time-dependent Semiclassics for Ultracold Bosons
• Quantum rotor theory of spinor condensates in tight traps
• Fisher information manifestation of dynamical stability and transition to self-trapping for Bose-Einstein condensates
• Stroboscopic aliasing in long-range interacting quantum systems
• Spontaneous symmetry breaking of binary fields in a nonlinear double-well structure
• Thermalization and its Breakdown for a Large Nonlinear Spin
• The open Bose-Hubbard chain: Pseudoclassical approach
• Understanding quantum work in a quantum many-body system
• Relevance of the resonance junctions on the Arnold web to dynamical tunneling and eigenstate delocalization
• Trojan quasiparticles
• Phase-space mixing in dynamically unstable, integrable few-mode quantum systems
• Eigenstate thermalization scaling in approaching the classical limit
• Fractional photon-assisted tunneling in an optical superlattice: large contribution to particle transfer
• Spatial two-particle NOON-states in periodically shaken three-well potentials
• Ground-state Properties of Small-Size Nonlinear Dynamical Lattices
• Spin squeezing in internal bosonic Josephson junctions via enhanced shortcuts to adiabaticity
• Adiabatic and non-adiabatic merging of independent Bose condensates
• On the Josephson effect in a Bose-Einstein condensate subject to a density dependent gauge potential
• Quantum and thermal fluctuations in bosonic Josephson junctions
• Twist-and-turn dynamics of spin squeezing in bosonic Josephson junctions: Enhanced shortcuts-to-adiabaticity approach
• Two-mode dipolar bosonic junctions
• Interaction-controlled impurity transport in trapped mixtures of ultracold bosons
• Fock space localization of polaritons in the Jaynes-Cummings dimer model
• Spread complexity and dynamical transition in multimode Bose-Einstein condensates
• Multimode N00N states in driven atomtronic circuits
• Stability limits for modes held in alternating trapping-expulsive potentials
• Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well
• Interaction-modulated tunneling dynamics in a mixture of Bose-Einstein condensates
• Symmetric and asymmetric localized modes in linear lattices with an embedded pair of ${\chi }^{(2)}$-nonlinear sites
• Soliton dynamics of an atomic spinor condensate on a Ring Lattice
• Fluctuations of the order parameter of a mesoscopic Floquet condensate
• Dynamical studies of macroscopic superposition states: Phase engineering of controlled entangled number states of Bose-Einstein condensate in multiple wells
• Quantum correlations of few dipolar bosons in a double-well trap
• Entangling two distinguishable quantum bright solitons via collisions
• Detecting Macroscopic Indefiniteness of Cat States in Bosonic Interferometers
• Correlation and entanglement of two-component Bose-Einstein condensates in a double well
• Resurgent revivals in bosonic quantum gases: a striking signature of many-body quantum interferences
• $N$-coherence vs. $t$-coherence: An alternative route to the Gross-Pitaevskii equation
• Heuristic approach to BEC self-trapping in double wells beyond mean-field
• Macroscopic quantum superpositon states of two-component Bose-Einstein condensates
• Number squeezed and fragmented states of strongly interacting bosons in a double well
• Phase-matching condition for enhanced entanglement of colliding indistinguishable quantum bright solitons in a harmonic trap
• Entropy production within a pulsed Bose-Einstein condensate
• Squeezed and fragmented states of strongly interacting bosons in a double well. Part II: Quantum Monte Carlo simulations
• Distinguishing mesoscopic quantum superpositions from statistical mixtures in periodically shaken double wells
• Comparative study of quantum dynamics of a few bosons in a one-dimensional split hard-wall trap: exact results versus Bose-Hubbard-model approximations
• Particle Correlations in Bose-Einstein Condensates
• Stationary states and quantum quench dynamics of Bose-Einstein condensates in a double-well potential
• Decay of symmetry-protected quantum states
• Probabilistic Hysteresis from a Quantum Phase Space Perspective
• A numerical study of the Bose-Einstein condensates in a double-well trap using finite differences
• Degree of simplicity of Floquet states of a periodically driven Bose-Hubbard dimer
• Josephson oscillation in the dissipative Bose-Hubbard dimer
• Arnold web and dynamical tunneling in a four-site Bose-Hubbard model