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arXiv:2408.12698 · Physica Scripta

Shape-controlled Bose–Einstein condensation

Cem Kurt, Altuğ Şişman, Alhun Aydin

Published Dec 16, 2024• 6 citations
arXivHTMLPDF

Abstract

Abstract Size-invariant shape transformation is a geometric technique that allows for a clear separation between quantum size and shape effects by modifying the shape of the confinement domain without altering its size. The impact of shape on the behavior of confined systems is significantly different from that of size, making it an emerging area of research. The recent realization of flat-bottomed optical box traps has further contributed to the study of quantum gases in complex confinement geometries. Here, we propose shape-induced Bose–Einstein condensation at a fixed size, temperature, and density. We investigate the impact of pure quantum shape effects on a non-interacting Bose gas confined within nested square domains, where the shape parameter is defined and controlled by the rotation angle between the inner and outer squares. Our findings reveal that specific heat exhibits an additional low-temperature peak at certain shapes. This work opens new avenues for controlling quantum systems through geometric manipulation and provides insights into the thermodynamic properties of Bose gases under shape-induced quantum effects.

DOI
10.1088/1402-4896/ad9fb2

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Abstract Size-invariant shape transformation is a geometric technique that allows for a clear separation between quantum size and shape effects by modifying the shape of the confinement domain without altering its size. The impact of shape on the behavior of confined systems is significantly different from that of size, making it an emerging area of research. The recent realization of flat-bottomed optical box traps has further contributed to the study of quantum gases in complex confinement geometries. Here, we propose shape-induced Bose–Einstein condensation at a fixed size, temperature, and density. We investigate the impact of pure quantum shape effects on a non-interacting Bose gas confined within nested square domains, where the shape parameter is defined and controlled by the rotation angle between the inner and outer squares. Our findings reveal that specific heat exhibits an additional low-temperature peak at certain shapes. This work opens new avenues for controlling quantum systems through geometric manipulation and provides insights into the thermodynamic properties of Bose gases under shape-induced quantum effects.
Bose–Einstein condensates (BECs) comprise a state of matter in which separate atoms or subatomic particles coalesce into a single macroscopic wave function when cooled to near absolute zero. BECs are confined within traps when carrying out experiments, and in the present paper, we model BECs confined within three-dimensional infinite potential wells corresponding to impenetrable boxes with prescribed geometric properties. To do this, we study the Gross–Pitaevskii equation (GPE) governing the macroscopic wave function within generic three-dimensional finite boxes, first describing analytical and numerical approaches for solving the ground state macroscopic wave function, and then employing these methods to understand how the geometry of a confining box influences properties of the BEC wave function. We show that the chemical potential of the BEC is sensitive to the size and shape of the box, with the chemical potential lowest for a spherical box and comparatively large for boxes with more extreme aspect ratios. Compared to commonly employed harmonic traps, geometrically confined BECs exhibit larger variations of the chemical potential with the self-interaction parameter, yet geometrically confined attractive BECs may be more robust against collapse. In particular, we show that the collapse threshold for an attractive BEC can be modified by the specific manner of geometric confinement.
Motivated by the expected realization of a shell shaped BEC in microgravity I studied the thermodynamics of bosonic quantum gases confined on the surface of a sphere both in the ideal and in the interacting case. In particular, once I found the values of the parameters of the external potential that are such to confine the gas to the surface of a sphere I computed the critical temperature as a function of the total number of atoms, the condensate and the thermal density as a function of the radius both in the ideal and interacting case and finally also the condensate and thermal fraction are computed.
The control over the geometry and topology of quantum systems is crucial for advancing novel quantum technologies. This work provides a synthesis of recent insights into the behavior of quantum vortices within atomic Bose–Einstein condensates (BECs) subject to curved geometric constraints. We highlight the significant impact of the curvature on the condensate density and phase distribution, particularly in quasi-one-dimensional waveguides for different angular momentum states. An engineered periodic transport of the quantized vorticity between density-coupled ring-shaped condensates is discussed. The significant role of curved geometry in shaping the dynamics of rotational Josephson vortices in long atomic Josephson junctions is illustrated for the system of vertically stacked toroidal condensates. Different methods for the controlled creation of rotational Josephson vortices in coupled ring systems are described in the context of the formation of long-lived vortex configurations in shell-shaped BECs with cylindrical geometry. Future directions of explorations of vortices in curved geometries with implications for quantum information processing and sensing technologies are discussed.
Shell-shaped Bose-Einstein condensate is a typical quantum system in curved geometry. Here, we propose a new type of shell-shaped Bose-Einstein condensate with a self-bound character, thereby liberating it from stringent conditions such as microgravity or a fine-tuned trap. Specifically, we consider a three-component (1, 2, 3) ultracold Bose gas where (1, 2) and (2, 3) both form quantum droplets. The two droplets are mutually immiscible due to strong 1-3 repulsion, while still linked by component-2 to form a globally self-bound object. The outer droplet then naturally develops a shell structure without any trapping potential. It is shown that the shell structure can significantly modify the equilibrium density of the core, and lead to unique collective excitations highlighting the core-shell correlation. All results have been demonstrated in a realistic ^{23}Na-^{39}K-^{41}K mixture. By extending quantum droplets from flat to curved geometries, this Letter paves the way for future explorations of the interplay of quantum fluctuations and nontrivial real-space topologies in ultracold gases.
Abstract Motivated by the recent experimental realization of ultracold quantum gases in shell topology, we propose a straightforward implementation of matter-wave lensing techniques for shell-shaped Bose–Einstein condensates. This approach allows to significantly extend the free evolution time of the condensate shell after release from the trap and enables the study of novel quantum many-body effects on curved geometries. With both analytical and numerical methods we derive optimal parameters for realistic schemes to conserve the shell shape of the condensate for times up to hundreds of milliseconds.
A shell-shaped Bose-Einstein condensate released from its confinement expands radially both outwards and inwards, displaying a self-interference pattern characterized by a density peak surrounded by a halo. Here we analyze how an external imprinting or the thermal fluctuations of the condensate phase influence this expansion. In both cases, we find that the curved geometry filters the imploding finite angular-momentum modes via a radial centrifugal potential, so that only the condensate state can reach the origin and form the central peak. As a consequence, we observe a pronounced dependence of the central density on the imprinting strength and on temperature. This geometric filtering effect characterizes the free expansion of curved atomic gases in contrast with flat counterparts, it is easily observable in the available experimental platforms, and enables two-dimensional shells thermometry via simple absorption-imaging techniques.