Momentum Distribution Dynamics of a Tonks-Girardeau Gas: Bragg Reflections of a Quantum Many-Body Wave Packet

We consider a strongly interacting quasi-one dimensional Bose gas on a tight ring trap subjected to a localized barrier potential. We explore the possibility to form a macroscopic superposition of a rotating and a nonrotating state under nonequilibrium conditions, achieved by a sudden quench of the barrier velocity. Using an exact solution for the dynamical evolution in the impenetrable-boson (Tonks-Girardeau) limit, we find an expression for the many-body wavefunction corresponding to a superposition state. The superposition is formed when the barrier velocity is tuned close to multiples of integer or half-integer number of Coriolis flux quanta. As a consequence of the strong interactions, we find that (i) the state of the system can be mapped onto a macroscopic superposition of two Fermi spheres, rather than two macroscopically occupied single-particle states as in a weakly interacting gas, and (ii) the barrier velocity should be larger than the sound velocity to better discriminate the two components of the superposition.

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“…It is defined in terms of the (time-dependent) one-body density matrix ρ 1 (x, y, t), which can be efficiently calculated according to [25] …”

Section: One-dimensional Momentum Distribution and Wigner Functionmentioning

confidence: 99%

Nonadiabatic creation of macroscopic superpositions with strongly correlated one-dimensional bosons in a ring trap

2011

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“…Therefore one can expect that the pseudopotential approximation will encapsulate much of the essential physics on the many-body level. In particular, the analytic accessibility of the pseudopotential model allows one to easily calculate the correlation functions and momentum distribution [26] of a TG gas in the presence of a localized impurity [25]. The pseudopotential model accurately describes the localized nature of the disturbance but due to its zero width nature it underestimates the size of the bubble.…”

mentioning

confidence: 99%

Ion-induced density bubble in a strongly correlated one-dimensional gas

et al. 2010

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We consider a harmonically trapped Tonks-Girardeau gas of impenetrable bosons in the presence of a single embedded ion, which is assumed to be tightly confined in an RF trap. In an ultracold ion-atom collision the ion's charge induces an electric dipole moment in the atoms which leads to an attractive r(-4) potential asymptotically. We treat the ion as a static deformation of the harmonic trap potential and model its short range interaction with the gas in the framework of quantum defect theory. The molecular bound states of the ionic potential are not populated due to the lack of any possible relaxation process in the Tonks-Girardeau regime. Armed with this knowledge we calculate the density profile of the gas in the presence of a central ionic impurity and show that a density bubble of the order of 1 mu m occurs around the ion for typical experimental parameters. From these exact results we show that an ionic impurity in a Tonks gas can be described using a pseudopotential approximation, allowing for significantly easier treatment

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“…In this paper, both for the optimization of (29) with respect to α and for the determination of B, Monte Carlo techniques are used (for N > 3). An exception is the case of g → 0 (the TG limit), where an effective algorithm presented by Pezer and Buljan [43] is used to determine the occupancies.…”

Section: The Von Neumann Entropymentioning

confidence: 99%

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

Kościk

2015

Physics Letters A

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We study one-dimensional systems of N particles in a one-dimensional harmonic trap with an inverse power law interaction ∼ |x| −d . Within the framework of the harmonic approximation we derive, in the strong interaction limit, the Schmidt decomposition of the one-particle reduced density matrix and investigate the nature of the degeneracy appearing in its spectrum. Furthermore, the ground-state asymptotic occupancies and their natural orbitals are derived in closed analytic form, which enables their easy determination for a wide range of values of N . A closed form asymptotic expression for the von Neumann entanglement entropy is also provided and its dependence on N is discussed for the systems with d = 1 (charged particles) and with d = 3 (dipolar particles).

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Momentum Distribution Dynamics of a Tonks-Girardeau Gas: Bragg Reflections of a Quantum Many-Body Wave Packet

Cited by 75 publications

References 44 publications

Nonadiabatic creation of macroscopic superpositions with strongly correlated one-dimensional bosons in a ring trap

Nonadiabatic creation of macroscopic superpositions with strongly correlated one-dimensional bosons in a ring trap

Ion-induced density bubble in a strongly correlated one-dimensional gas

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

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