Quantum simulation of expanding space–time with tunnel-coupled condensates

Abstract

We consider two weakly interacting quasi-1D condensates of cold bosonic atoms. It turns out that a time-dependent variation of the tunnel-coupling between those condensates is equivalent to the spatial expansion of a one-dimensional toy-Universe, with regard to the dynamics of the relative phase field. The dynamics of this field is governed by the quantum sine-Gordon equation. Thus, this analogy could be used to 'quantum simulate' the dynamics of a scalar, interacting quantum field on an expanding background. We discuss how to observe the 'freezing' of quantum fluctuations during an accelerating expansion in a possible experiment. We also analyze an experimental protocol to study the formation of sine-Gordon breathers in the relative phase field, seeded by quantum fluctuations. IntroductionThe recent progress in coherently controlling systems of cold atoms (e.g., [1-5]), stimulated a lot of research concerned with employing these experimental systems to 'quantum simulate' prototypical quantum manybody models and quantum field theories (e.g., [6,7]). This includes dynamics that is relevant for the early Universe, e.g. the initial acoustic density oscillations (Sakharov oscillations) that determine the structure observed in the cosmic microwave background radiation and which have recently been simulated using a quench in a cloud of cold atoms [8]. Particularly fascinating are ideas concerned with simulating quantum many-body physics on curved space-times ('analog gravity') (see [9][10][11][12][13][14][15][16][17][18][19][20], as well as references therein) connecting concepts and techniques from cosmology and condensed matter.During the past few years, a very versatile platform for analog quantum simulations with cold atoms has been established in the Schmiedmayer group at Vienna: an atom chip holding one or two quasi-1D bosonic condensates [3,[21][22][23]. In this setup, it is possible to tune the trapping potential in a time-dependent fashion, which includes the possibility to modify the tunnel-coupling between two nearby condensates. That has been used experimentally to probe quench physics [24-28] and to control non-equilibrium dynamics [29]. After releasing the trap, the expanding clouds give rise to matter-wave interference that reveals the relative phase between the two condensates. The spatially resolved phase field can be measured for each run of the experiment, and the full statistics [22,30] as well as higher-order correlators [28] have been extracted from the data of many runs. A recent comprehensive overview of this set of experiments can be found in [31]. The opportunities offered by this platform have resulted in a number of theoretical proposals for future experiments, e.g. [32][33][34].In the present work, we argue that a pair of tunnel-coupled, quasi-1D, bosonic condensates can be employed for simulating an interacting, scalar quantum field on top of an expanding 1+1 dimensional space-time (figures 1(a) and (c)). This scalar field is represented by the relative phase field between the condensate...

Analog of cosmological particle creation in electromagnetic waveguides

“…5 provides plots of the correlation function κ(t 1 , x 1 , t 2 , x 2 ) for two fixed pairs of identical positive times t 1 = t 2 . The singularities characterized by the second line of equation (15) occur along the black rectangle appearing in both of these plots. As a function of time, the corners of this structure continuously move along the boundaries of the domain [0, D] 2 .…”

“…[4] (see also [39] for technical details). Again, we study the expression κ(t 1 , x 1 , t 2 , x 2 ) and analyze its behavior along the characteristic lines specified by equation (15). This involves several approximations that are further discussed in Appendix B.…”

“…Since the arctangent adopts finite values for all real arguments, the expression κ B never diverges. This finding requires all singularities obeying the second line of equation (15) to be smoothened out for continuous profiles v(t).…”

“…As direct experimental tests of cosmological particle creation are probably out of reach, several laboratory analogs [6][7][8] for quantum fields in expanding space-times have been proposed for various scenarios, including Bose-Einstein condensates [9][10][11][12][13][14][15][16], ion traps [17][18][19][20], and electromagnetic waveguides [21]. In the following, we shall consider the latter system (see also [22]), which has already been used to observe an analog of the closely related dynamical Casimir effect [21,[23][24][25][26].…”

Focus on gravitational quantum physics

“…Westerberg et al show that time-dependent spacetimes can be simulated by using intense tailored laser pulses that modify the refractive index of an optical medium [21]. In a similar vein, Neuenhahn and Marquardt describe how expanding spacetimes can be simulated via time-dependent variation of the tunnel-coupling between two weakly interacting quasi-1D condensates of cold bosonic atoms [22].…”