Rotonlike Instability and Pattern Formation in Spinor Bose-Einstein Condensates

Abstract

We show that metastable phases of an antiferromagnetic spin-1 condensate in a simple model with pure contact interactions can exhibit a rotonlike minimum in the excitation spectrum. The introduction of magnetic field gives rise to the instability of roton modes, which can lead to spontaneous emergence of regular periodic, polygonal, polyhedral or crystalline patterns, as shown in numerical simulations within the truncated Wigner approximation. An explanation of the occurrence of rotonlike instability is given based on the energy and spin conservation laws.PACS numbers: 03.75. Kk, 03.75.Mn, 67.85.De, 67.85.Fg Bose-Einstein condensates with spin degrees of freedom [1] attracted in recent years great interest due to the unique possibility of exploring fundamental concepts of quantum mechanics in a remarkably controllable and tunable environment. The ability to generate spin squeezing and entanglement [2] makes spinor Bose gases promising candidates for applications as quantum simulators [3], in quantum information [4], and for precise measurements [5]. Moreover, spinor condensates were successfully used to recreate many of the phenomena of condensed matter physics in experiments displaying an unprecedented level of control over the quantum system. In particular, spin domains [6], spin mixing [7], and spin vortices [8] were predicted and observed.The fundamental concept of a roton excitation, first introduced by Landau in the context of superfluid helium, is crucial for understanding of its physical properties [9]. It is characterized by a minimum in the spectrum of excitations occurring at a finite wavelength,. If the roton gap ∆ can be decreased by changing the system parameters, the softening of the roton mode can eventually lead to an instability. This instability scenario is encountered also in many other branches of quantum physics, including strongly correlated Fermions [10], quantum Hall systems [11], and Bose-Einstein condensates with long range interactions [12][13][14]. The roton instability is characterized by unstable modes with wavevector lengths close to the roton minimum k 0 . It was suggested that it can lead to the emergence of the peculiar supersolid state [15], and several other physical phenomena [16].Here, we show that rotonlike instability can occur in spinor Bose-Einstein condensates in a simple model with pure contact interactions. It can take place in appropriately prepared metastable states of an antiferromagnetic spin-1 condensate [17] under the influence of magnetic field. Moreover, we show that, depending on the geometry and the trapping potential, it can lead to spontaneous emergence of variety of transient ordered patterns, including polygonal, polyhedral and crystalline structures. We show that these results can be verified in experiments with 23 Na condensate, which is characterized by very weak dipolar interactions [18]. We provide an explanation for the occurrence of rotonlike instability based on energy and spin conservation laws, and demonstrate how the pattern characteristic...

Crossover from weak to strong quench in a spinor Bose-Einstein condensate

“…Using a sample containing an enhanced seed for long-wavelength spin excitations, we demonstrate that the long-wavelength instability is strongly suppressed for a strong quench with q > 2. We find that the observed crossover of the earlytime post-quench dynamics is consistent with the Bogoliubov description of the dynamic instability of the initial EPP state [13,14]. Our results demonstrate the different quantum-quench regimes for a spinor BEC system.…”

Patterns and excitations in antiferromagnetic spinor condensates

“…To model the above quantum system numerically in an efficient way, we applied the truncated Wigner approximation [11,23,35] to describe the evolution. The initial state was perturbed by spectrally limited noise to account for quantum fluctuations and density profile imperfections [20,29]. We achieve a very good agreement between analytical, numerical, and experimental [36] results for both the wave-vector length Fig.…”

“…This is because of spin conservation, which ensures that the condensate remains maximally polarized in the transverse direction [29]. The situation changes after introducing the magnetic field, which breaks the transverse spin conservation.…”

Stability of nonstationary states of spin-1 Bose-Einstein condensates

“…There are a few theoretical studies where the stability analysis has been extended to nonstationary states: The effects of a nonzero magnetic field on the stability of states with timeindependent spin populations but oscillating relative phases have been examined in Refs. [16][17][18]. Although the spin populations remain constant throughout the time evolution, these states are nonstationary because the relative phases of the spin components vary in time.…”