Coherent backscattering in the Fock space of ultracold bosonic atoms

Schlagheck, Peter; Dujardin, Julien

doi:10.1002/andp.201600311

Cited by 3 publications

(8 citation statements)

References 49 publications

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“…Before continuing we simplify the notation by subsuming position and momentum coordinates into single phase-space variables X ≡ (R, P) (48) of 2L components and similarly…”

Section: Final Resultsmentioning

confidence: 99%

“…In particular, we investigate return probabilities where the final and initial state are equal. This is particularly interesting for the investigation of (dynamical) localization effects [14][15][16][17][18][19][20][21], modal echo [44][45][46], many-body coherent backscattering [47][48][49], (dynamical) tunneling [17,22,23] in mean-field space [24,25], or quantum manybody scarring [6][7][8][9]26], for which the associated characteristic enhancement signatures in the return probability can be discriminated from purely symmetry-related enhancement by our method.…”

Section: Application In Many-body Scenariosmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented truncated Wigner method

Hummel¹,

Schlagheck²

2022

J. Phys. A: Math. Theor.

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Although highly successful, the Truncated Wigner Approximation (TWA) does not account for genuine many-body quantum interference between different solutions of the mean-field equations of a bosonic many-body (MB) system. This renders the TWA essentially classical, where a large number of particles formally takes the role of the inverse of Planck's constant $\hbar$. The failure to describe genuine interference phenomena, such as localization and scarring in Fock space, can be seen as a virtue of this quasiclassical method, which thereby allows one to identify genuine quantum effects when being compared with ``exact'' quantum calculations that do not involve any a priori approximation. A rather prominent cause for such quantum effects that are not accounted for by the TWA is the constructive interference between the contributions of symmetry-related trajectories, which would occur in the presence of discrete symmetries provided the phase-space distribution of the initial state and the observable to be evaluated feature a strong localization about the corresponding symmetry subspaces. Here we show how one can conceive an augmented version of the TWA which can account for this particular effect. This augmented TWA effectively amounts to complementing conventional TWA calculations by separate Truncated Wigner simulations that are restricted to symmetric subspaces and involve weight factors that account for the dynamical stability of sampling trajectories with respect to perpendicular deviations from those subspaces. We illustrate the validity of this method at pre- as well as post-Ehrenfest time scales in prototypical Bose-Hubbard systems displaying chaotic classical dynamics, where it also reveals the existence of additional MB interference effects.

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“…Before continuing we simplify the notation by subsuming position and momentum coordinates into single phase-space variables X ≡ (R, P) (48) of 2L components and similarly…”

Section: Final Resultsmentioning

confidence: 99%

Section: Application In Many-body Scenariosmentioning

confidence: 99%

Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented truncated Wigner method

Hummel¹,

Schlagheck²

2022

J. Phys. A: Math. Theor.

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show abstract

“…The comparison with the exact quantum return probabilities also revealed significant deviations for very long evolution times, which we attribute to additional quantum effects coming into play. Possible causes could be (dynamical) quantum tunneling [17,22,23] in mean-field space [24,25], many-body coherent backscattering [41][42][43], a modal echo [38][39][40], (dynamical) localization effects [14][15][16][17][18][19][20][21], or many-body quantum scarring [6][7][8][9]26], depending on the underlying (regular or chaotic) classical phase-space structure. Rather than considering the failure to reproduce those effects as an intrinsic shortcoming of the presented method, we believe, on the contrary, that the augmented TWA can serve as a valuable indicator for the relevance of one or several of those genuinely quantum phenomena.…”

Section: Discussionmentioning

confidence: 99%

“…In particular, we investigate return probabilities where the final and initial state are equal. This is particularly interesting for the investigation of (dynamical) localization effects [14][15][16][17][18][19][20][21], modal echo [38][39][40], many-body coherent backscattering [41][42][43], (dynamical) tunneling [17,22,23] in meanfield space [24,25], or quantum many-body scarring [6][7][8][9]26], for which the associated characteristic enhancement signatures in the return probability can be discriminated from purely symmetry-related enhancement by our method.…”

Section: Application In Many-body Scenariosmentioning

confidence: 99%

“…Opposite cases corresponding to an underestimation of the average long-time return probability by the augmented TWA, leading to a "super enhancement" beyond the maximal possible symmetry enhancement factor (see, e.g., figure 3a and figure 3b), can be indicative of an interference-induced inhibition of quantum transport due to dynamical features, related to (dynamical) localization [14][15][16][17][18][19][20][21] or quantum many-body scarring [6][7][8][9]26]. Coherent backscattering [41][42][43] and the manifestation of a modal echo [38][39][40] can be additional causes for such an enhancement of the return probability.…”

Section: Deviation In the Long-time Saturationmentioning

confidence: 99%

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Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented Truncated Wigner method

Hummel¹,

Schlagheck²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Although highly successful, the Truncated Wigner Approximation (TWA) does not account for genuine many-body quantum interference between different solutions of the mean-field equations of a bosonic many-body (MB) system. This renders the TWA essentially classical, where a large number of particles formally takes the role of the inverse of Planck's constant . The failure to describe genuine interference phenomena, such as localization and scarring in Fock space, can be seen as a virtue of this quasiclassical method, which thereby allows one to identify genuine quantum effects when being compared with "exact" quantum calculations that do not involve any a priori approximation. A rather prominent cause for such quantum effects that are not accounted for by the TWA is the constructive interference between the contributions of symmetry-related trajectories, which would occur in the presence of discrete symmetries provided the phase-space distribution of the initial state and the observable to be evaluated feature a strong localization about the corresponding symmetry subspaces. Here we show how one can conceive an augmented version of the TWA which can account for this particular effect. This augmented TWA effectively amounts to complementing conventional TWA calculations by separate Truncated Wigner simulations that are restricted to symmetric subspaces and involve weight factors that account for the dynamical stability of sampling trajectories with respect to perpendicular deviations from those subspaces. We illustrate the validity of this method at pre-as well as post-Ehrenfest time scales in prototypical Bose-Hubbard systems displaying chaotic classical dynamics, where it also reveals the existence of additional MB interference effects.

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Tunneling control in an integrable model for Bose-Einstein Condensate in a triple well potential

Ymai¹,

Tonel²

2017

Preprint

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In this work we show the simplest and integrable model for Bose-Einstein condensates loaded in a triple well potential where the tunneling between two wells can be controlled by the other well showing a behavior similar to an electronic field effect transistor. Using a classical analysis, the Hamilton's equation are obtained, a threshold indicating a discontinuous phase transition is presented and the classical dynamics is computed. Then, the quantum dynamics is investigated using direct diagonalization. We find well agreement in both these analysis. Based on our results, the switching scheme for tunneling is shown and the experimental feasibility is discussed.

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Coherent backscattering in the Fock space of ultracold bosonic atoms

Cited by 3 publications

References 49 publications

Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented truncated Wigner method

Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented truncated Wigner method

Symmetry-induced many-body quantum interference in chaotic bosonic systems: an augmented Truncated Wigner method

Tunneling control in an integrable model for Bose-Einstein Condensate in a triple well potential

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