Many-body exceptional points in colliding condensates

ABSTRACT

Exceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier et al., Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose–Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of superfluidity and to the scattering of classical particles. We propose an experimental set-up to directly probe this exceptional point, and demonstrate its feasibility with the aid of numerical calculations. Our work fosters the observation of exceptional points in nonequilibrium many-body quantum systems.

GRAPHICAL ABSTRACT

Keywords:

• Many-body quantum
• dynamics
• exceptional points
• counterflow instability
• superfluidity

Acknowledgments

The authors acknowledge useful discussions with Frederic Chevy and Arnaud Courvoisier. The authors thank Yonathan Japha for sharing his code for the efficient numerical solution of the GPE.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Emanuele G. Dalla Torre  http://orcid.org/0000-0002-7219-3804

Notes

1 According to the classification of Cross and Hohenberg [43], patterns of type I have a finite wavevector and ‘o’ stands for oscillatory.

2 Interestingly, at that time only one material, He⁴, was known to Bose condense. Ref. [4] indeed mentions:

Let us note at once, however, that there apparently does not exist on this planet a solution of two Bose liquids such that both components do not solidify before the λ transition. The only other candidate besides He⁴, namely He⁶, is radioactive (half-life 0.8 s). But besides possible astrophysical applications, such a simple microscopic model is of interest, since it may help us understand the general laws typical of solutions of two superfluid liquids. For example, the presence of two Bose branches in the spectrum of the elementary excitations is typical of both Bose–Bose and Fermi–Bose superfluid mixtures.

It is quite remarkable that more than 40 years later, this theoretical work has become relevant to actual experiments on this planet.

3 These modes have been recently probed experimentally by Ref. [44].

4 Conuterflowing superfluids were studied both theoretically and experimentally in earlier works. See in particular theoretical studies concerning the counterflow instability in Mott insulators [45], normal fluids [46], and in higher dimensions, where mean-field applies [47]. In two dimensions, numerical simulations reveal that the excitations have the form of vortex-antivortex pairs, and eventually lead to a chaotic motion of the particles [48–50]. See also the famous quantum Newton's cradle experiment for the case of the counterflow between two condensates made of identical atoms [51], and experiments of atomic-pair generation in colliding condensates [52,53].

5 See Refs. [6,7] for the relation between this expression and the Landau criterion of a Fermi superfluid.

6 See Ref. [54] for an introduction

7 See Ref. [55] for an introduction.

8 This distinction is due to the fact that the GPE involves complex wavefunctions. In contrast, in the case of a classical modes, such as elastic waves, the positive and negative branches are physically identical.

9 See Ref. [56] for a recent review of these experiments.

10 To facilitate the analysis of the dynamics, movies were also created and are available at http://nonequilibrium.ph.biu.ac.il/thesis/.

Additional information

Funding

This research is supported by the Israel Science Foundation [grant number 1452/14].