Negative-Mass Hydrodynamics in a Spin-Orbit–coupled Bose-Einstein Condensate

Abstract

A negative effective mass can be realized in quantum systems by engineering the dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently at the center of intense research efforts. Here we measure an expanding spin-orbit coupled Bose-Einstein condensate whose dispersion features a region of negative effective mass. We observe a range of dynamical phenomena, including the breaking of parity and of Galilean covariance, dynamical instabilities, and self-trapping. The experimental findings are reproduced by a single-band Gross-Pitaevskii simulation, demonstrating that the emerging features -shockwaves, soliton trains, self-trapping, etc.-originate from a modified dispersion. Our work also sheds new light on related phenomena in optical lattices, where the underlying periodic structure often complicates their interpretation.

Positive and Negative Particle Masses in the Bicubic Equation Limiting Particle Velocity Formalism

“…The announcement by Gaal (2017) of the effective negative mass observation by Khamehchi et al (2017) in a spin-orbit coupled Bose -Einstein condensate immediately raises a question, is this an isolated case or is it generally allowed, say by the bicubic equation limiting particle velocity formalism (Śoln, 2014, 2015, 2016, 2017).…”

“…Here, rather than get involved into the complexity as to why and how the negative mass m − ≺ 0 occurred in Khamehchi et al (2017) and more recently in Li & Cui (2017) and Dold (2017), one would like to see how the expressions for limiting velocities c 1 , c 2 and c 3 change when an explicitly negative mass m − = −m 0 is introduced. Working with |z| ≺≺ 1, one finds specifically that the obscure particle, when one changes m + → −m ≺ 0, assumes the primary particle form with positive rest energy and positive kinetic energy, with its c 2 becoming real, c Because of the small congruent parameter values, |z| ≺≺ 1, with m + → −m, m ≻ 0, the normal particle only implicitly indicates that it still has positive rest energy and positive kinetic energy with c 3 remaining real.…”

The One-Dimensional, Non-Relativistic, Quanitum Morse Oscillator at the Classical Limit

“…On the other hand, we should remark that a relativistic quantum formulation of the same, say, type as our formulation could be useful to explain phenomena as described in refs. [4,5]. Finally, one would mention refs.…”

“…In this context, negative mass can exist, for example, in non-asymptotically flat space-time [4]. On the other hand, negative mass has been found in a Bose condensate fluid [5]. Finally, we can find negative effective electron mass in semiconductor superlattices [1][2][3].…”

“…The one-dimensional case will be regarded. In addition, as notorious and interesting examples, we will discuss the role of electrons of negative mass in semiconductor superlattices [1][2][3] and, on the other hand, we will comment on cosmological as well as on Bose condensates and various elementary-particle questions dealing with the possibility of negative rest-mass [4,5]. In particular, with respect to semiconducting superlattices, we note that the fact that there are electrons with negative rest-mass mass in these structures comes from the existence of allowed and forbidden minibands formed from allowed and forbidden energy bands [1][2][3].…”