Superballistic center-of-mass motion in one-dimensional attractive Bose gases: Decoherence-induced Gaussian random walks in velocity space

Abstract

We show that the spreading of the center-of-mass density of ultracold attractively interacting bosons can become superballistic in the presence of decoherence, via single-, two-and/or three-body losses. In the limit of weak decoherence, we analytically solve the numerical model introduced in [Phys. Rev. A 91, 063616 (2015)]. The analytical predictions allow us to identify experimentally accessible parameter regimes for which we predict superballistic spreading of the center-of-mass density. Ultracold attractive Bose gases form weakly bound molecules; quantum matter-wave bright solitons. Our computer-simulations combine ideas from classical field methods ("truncated Wigner") and piecewise deterministic stochastic processes. While the truncated Wigner approach to use an average over classical paths as a substitute for a quantum superposition is often an uncontrolled approximation, here it predicts the exact root-mean-square width when modeling an expanding Gaussian wave packet. In the superballistic regime, the leading-order of the spreading of the center-of-mass density can thus be modeled as a quantum superposition of classical Gaussian random walks in velocity space.

Truncated Wigner dynamics and conservation laws

“…It has been treated with the truncated Wigner method [14]. There are recent claims that this approximation exactly replicates quantum center-ofmass position spreading [15,16]. We find that while the errors are small, this result is not exact.…”

Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

“…First, we introduce the star product [74]: When transforming to phase space, one has to replace the product  B of two Hilbert space operators  and B by their star product A ⋆ B , which is defined as [75] Here, the arrows indicate in which direction the derivatives act. The star product (6) allows to introduce the Moyal bracket [74,76] (2)…”

“…Thus, we can assume that we work in the classical limit where quantum effects apart from collapses (which, in the Fokker-Planck approximation, correspond to momentum diffusion) are negligible, such that particles have well-defined trajectories that can be described using Langevin equations. 6 The Langevin equations corresponding to the Fokker-Planck equation (20) read where ⃗ 𝜒 i (t) is white noise with the properties with the ensemble average ⟨⋅⟩ E , dyadic product ⊗ , and identity matrix 1 . Thus, we can base our simulations on the Langevin equations ( 51) and ( 52).…”

“…Wigner functions provide a description of quantum systems in phase space. Since their initial development [1], they have found a significant number of applications [2][3][4][5] in fields such as atomic physics [6], quantum optics [7][8][9], visualization of quantum effects [10,11], computational electronics [12][13][14], and solid-state theory [15][16][17][18][19]. Besides these practical aspects, they are also of interest for fundamental questions in quantum mechanics such as the theory of quantum chaos [20].…”

Master equations for Wigner functions with spontaneous collapse and their relation to thermodynamic irreversibility

“…(6) Here, the arrows indicate in which direction the derivatives act. The star product (6) allows to introduce the Moyal bracket [74,76] {A(x, p), B(x, p)}…”