Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Alon, Ofir E.

doi:10.3390/sym11111344

Cited by 23 publications

(51 citation statements)

References 107 publications

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“…Dealing with finite systems, it is usually necessary to resort to numerical calculations. Thus powerful numerical methods have been developed for studying the dynamics of finite Bose systems [ 143 , 144 , 145 ]. Hopefully, the described notions could be successfully employed for the analysis of finite systems by applying numerical methods.…”

Section: Discussionmentioning

confidence: 99%

Order Indices and Entanglement Production in Quantum Systems

Yukalov

2020

Entropy

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The review is devoted to two important quantities characterizing many-body systems, order indices and the measure of entanglement production. Order indices describe the type of order distinguishing statistical systems. Contrary to the order parameters characterizing systems in the thermodynamic limit and describing long-range order, the order indices are applicable to finite systems and classify all types of orders, including long-range, mid-range, and short-range orders. The measure of entanglement production quantifies the amount of entanglement produced in a many-partite system by a quantum operation. Despite that the notions of order indices and entanglement production seem to be quite different, there is an intimate relation between them, which is emphasized in the review.

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Section: Discussionmentioning

confidence: 99%

Order Indices and Entanglement Production in Quantum Systems

Yukalov

2020

Entropy

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“…We solve the time-dependent many-boson Schrödinger equation presented in Eq. (1) using the MCTDHB method 36,39,40,49,57,58,61,[65][66][67][68][69][70][71][72][73][73][74][75][76][77][78][79][80][81][82] . The method is well documented and applied in the literature 59 .…”

Section: System and Methodologymentioning

confidence: 99%

Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction

Bhowmik

Halder

Alon

2020

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Tunneling in a many-body system appears as one of the novel implications of quantum physics, in which particles move in space under an otherwise classically-forbidden potential barrier. Here, we theoretically describe the quantum dynamics of the tunneling phenomenon of a few intricate bosonic clouds in a closed system of a two-dimensional symmetric double-well potential. We examine how the inclusion of the transverse direction, orthogonal to the junction of the double-well, can intervene in the tunneling dynamics of bosonic clouds. We use a well-known many-body numerical method, called the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. MCTDHB allows one to obtain accurately the time-dependent many-particle wavefunction of the bosons which in principle entails all the information of interest about the system under investigation. We analyze the tunneling dynamics by preparing the initial state of the bosonic clouds in the left well of the double-well either as the ground, longitudinally or transversely excited, or a vortex state. We unravel the detailed mechanism of the tunneling process by analyzing the evolution in time of the survival probability, depletion and fragmentation, and the many-particle position, momentum, and angular-momentum expectation values and their variances. As a general rule, all objects lose coherence while tunneling through the barrier and the states which include transverse excitations do so faster. In particular for the later states, we show that even when the transverse direction is seemingly frozen, prominent many-body dynamics in a two-dimensional bosonic Josephson junction occurs. Implications are briefly discussed.

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“…This maximal entropy for small

implies that the Hilbert space provided by MCTDH-X is not large enough to host the complete dynamics of the many-body wave functions and more orbitals (

) would therefore be necessary to achieve convergence. Based on the FGH results for sudden switches of the potential barrier, to cover the subspace of the Hilbert space more than

(corresponding to a maximal entropy of

) orbitals are necessary, which exceeds the typically employed number of orbitals (

) for

bosons reported in the literature [ 74 , 75 ]. While the quantitative behavior of the entropy

at small

in Figure 14 c,f therefore cannot be considered fully converged, the observed behavior is qualitatively equivalent to that resulting for smaller particle numbers, where convergence of MCTDH-X could be achieved with a smaller number

of orbitals, and is also consistent with our FGH-based analysis for

particles (see Figure 12 ).…”

Section: Dynamics In the Double-wellmentioning

confidence: 99%

Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

Schäfer

Bastarrachea-Magnani

Lode

et al. 2020

Entropy

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We examine the spectral structure and many-body dynamics of two and three repulsively interacting bosons trapped in a one-dimensional double-well, for variable barrier height, inter-particle interaction strength, and initial conditions. By exact diagonalization of the many-particle Hamiltonian, we specifically explore the dynamical behaviour of the particles launched either at the single particle ground state or saddle point energy, in a time-independent potential. We complement these results by a characterisation of the cross-over from diabatic to quasi-adiabatic evolution under finite-time switching of the potential barrier, via the associated time-evolution of a single particle's von Neumann entropy. This is achieved with the help of the multiconfigurational time-dependent Hartree method for indistinguishable particles (Mctdh-x) -which also allows us to extrapolate our results for increasing particle numbers.

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Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

Cited by 23 publications

References 107 publications

Order Indices and Entanglement Production in Quantum Systems

Order Indices and Entanglement Production in Quantum Systems

Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction

Spectral Structure and Many-Body Dynamics of Ultracold Bosons in a Double-Well

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