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Journal of Experimental and Theoretical Physics Letters

Structural properties of the condensate in two-dimensional mesoscopic systems of strongly correlated excitons

Yu. E. Lozovik, S. Yu. Volkov, M. Willander

Published May 1, 2004• 28 citations
Publisher

Abstract

A two-dimensional mesoscopic Bose system of dipoles in a 2D trap is considered using computer simulation by the quantum path-integral Monte Carlo method. The model describes a rarefied system of spatially indirect excitons in a confining potential. Bose condensation in the system and its superfluid and structural properties are studied over a wide range of interparticle spatial correlations, from an almost ideal Bose gas to the regime of a strongly correlated system. It is found that, at strong interparticle spatial correlations, particles in the condensate form a crystal-like structure. In this case, the spatial correlations of particles in the condensate are less pronounced than the correlations of noncondensed particles. The effect of recurrent crystallization is observed in the regime of strong interparticle correlations.

DOI
10.1134/1.1780555

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A two-dimensional mesoscopic Bose system of dipoles in a 2D trap is considered using computer simulation by the quantum path-integral Monte Carlo method. The model describes a rarefied system of spatially indirect excitons in a confining potential. Bose condensation in the system and its superfluid and structural properties are studied over a wide range of interparticle spatial correlations, from an almost ideal Bose gas to the regime of a strongly correlated system. It is found that, at strong interparticle spatial correlations, particles in the condensate form a crystal-like structure. In this case, the spatial correlations of particles in the condensate are less pronounced than the correlations of noncondensed particles. The effect of recurrent crystallization is observed in the regime of strong interparticle correlations.
A mesoscopic system of dipolar bosons trapped by a harmonic potential is considered. The system has a number of physical realizations including dipole excitons, atoms with large dipolar moment, polar molecules, and Rydberg atoms in inhomogeneous electric field. We carry out a diffusion Monte Carlo simulation to define the quantum properties of a two-dimensional system of trapped dipoles at zero temperature. In dimensionless units the system is described by two control parameters, namely, the number of particles and the strength of the interparticle interaction. We have shown that when the interparticle interaction is strong enough a mesoscopic crystal is formed. As the strength of interactions is decreased a multistage melting takes place. Off-diagonal order in the system is tested using natural-orbitals analysis. We have found that the system might be Bose condensed even in the case of strong interparticle interactions. There is a set of parameters for which a spatially ordered structure is formed while simultaneously the fraction of Bose-condensed particles is nonzero. This might be considered as a realization of a mesoscopic supersolid.
Low-temperature properties of harmonically confined two-dimensional assemblies of dipolar bosons are systematically investigated by Monte Carlo simulations. Calculations carried out for different numbers of particles and strengths of the confining potential yield evidence of a quantum phase transition from a superfluid to a crystal-like phase, consistently with what is observed in the homogeneous system. It is found that the crystal phase nucleates in the center of the trap, as the density increases. Bose-Einstein condensation vanishes at T=0T=0T=0 upon entering the crystalline phase, concurrently with the disappearance of the superfluid response.
We present a Quantum Monte Carlo study of the ground state properties of a two dimensional system of Bose particle with dipole moment in a harmonic trap. The direction of the dipoles is assumed to be fixed by an external field. We study how the system behaves when the direction of the dipole moments is changed. Our analysis is made using Path Integral Monte Carlo simulations in the Grand Canonical ensemble, using the Worm Algorithm. We study systems of increasing size, focusing on the spatial distribution of the atoms inside the trap and on the superfluid fraction of the sample. We find that vertical dipoles form a crystal, characterized by a shell structure, while tilting the dipoles has the effect of inducing a striped structure. We find that similar behaviour can be found in the analogue classical system. Vertical dipoles display nonclassical inertia while a strong tilting decreases superfluidity.
Using the finite-temperature path integral Monte Carlo method, we investigate dilute, trapped Bose gases in a quasi-two-dimensional (quasi-2D) geometry. The quantum particles have short-range, sss-wave interactions described by a hard-sphere potential whose core radius equals its corresponding scattering length. The effect of both the temperature and the interparticle interaction on the equilibrium properties such as the total energy, the density profile, and the superfluid fraction is discussed. We compare our accurate results with both the semiclassical approximation and the exact results of an ideal Bose gas. Our results show that for repulsive interactions (i) the minimum value of the aspect ratio, where the system starts to behave quasi-2D, increases as the two-body interaction strength increases; (ii) the superfluid fraction for a quasi-two-dimensionally Bose gas is distinctly different from that for both a quasi-1D Bose gas and a true 3D system, i.e., the superfluid fraction for a quasi-2D Bose gas decreases faster than that for a quasi-1D system and a true 3D system with increasing temperature, and shows a stronger dependence on the interaction strength; (iii) the superfluid fraction for a quasi-2D Bose gas lies well below the values calculated from the semiclassical approximation; and (iv) the Kosterlitz-Thouless transition temperature decreases as the strength of the interaction increases.
Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose–Einstein condensation temperature T c , as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality d and on the confining dimension D of the system. The consideration shows that mesoscopic systems, experiencing Bose–Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension d > 2 above T c and in a box of d > 4 below T c ; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension D > 2 above T c and of a confining dimension D > 4 below T c ; (iii) the interacting Bose system is confined in a rectangular box of dimension d > 2 above T c , while below T c , particle interactions stabilize the Bose-condensed system, making it stable for d = 3 ; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions.
Confined indirect excitons in a two-dimensional magnetic lattice are promoted to simulate condensed matter systems. Excitonic particles are magnetically trapped so that a sufficient cooling mechanism can allow the trapped clouds of indirect excitons to experience the Bose-Einstein condensation phase transition. Thus, a long­ range spatial coherence can be resolved causing an inherited phase-locked across all of the coupled sites (single traps). Using an external magnetic bias field a mutual tunneling can adiabatically be exchanged between sites in which case the underline physics of Bose-Hubbard model can be explored such as Mott-insulator and Josephson Effect.