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Momona Ethiopian Journal of Science

Quantum Fluctuations of Low Dimensional Bose-Einstein Condensates in Optical Systems

A. Mebrahtu

Published Jul 7, 2011• 0 citations
Publisher

Abstract

A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have investigated the theory and manifestation of fluctuations in quantum optical systems in low dimensional Bose-Einstein condensates. We have described the system using the mean-field approximation. In this study we have verified that low dimensional quantum gases exhibit not only highly fascinating properties but also we have indicated that the use of mean field theory to describe quantum gases in low dimensions is highly restricted since the possibility of generating low dimensional bosonic condensates is dominated by the existence of highly sensitive and intrinsic quantum fluctuations.

DOI
10.4314/mejs.v3i2.67709

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A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have investigated the theory and manifestation of fluctuations in quantum optical systems in low dimensional Bose-Einstein condensates. We have described the system using the mean-field approximation. In this study we have verified that low dimensional quantum gases exhibit not only highly fascinating properties but also we have indicated that the use of mean field theory to describe quantum gases in low dimensions is highly restricted since the possibility of generating low dimensional bosonic condensates is dominated by the existence of highly sensitive and intrinsic quantum fluctuations.
A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.
In this thesis, we have investigated several fluctuation-driven phenomena in ultracold spinor Bose gases. In Bose-Einstein condensates of hyperfine spin-two (F=2) atoms, it is shown that zero-point quantum fluctuations completely lift the accidental continuous degeneracy in quantum spin nematic phases predicted by mean field analysis, and these fluctuations select out two distinct spin nematic states with higher symmetries. It is further shown that fluctuations can drive a novel type of coherent spin dynamics which is very sensitive to the variation of quantum fluctuations controlled by magnetic fields or potential depths in optical lattices. These results have indicated fundamental limitations of precision measurements based on mean field theories. In addition, fluctuation-driven coherent spin dynamics studied here is a promising tool to probe correlated fluctuations in many body systems. In another system -- a two-dimension superfluid of spin-one (F=1) Na²³ atoms -- we have investigated spin correlations associated with half quantum vortices. It is shown that when cold atoms become superfluid below a critical temperature a unique nonlocal topological order emerges simultaneously due to fluctuations in low dimensional systems. Our simulation have indicated that there exists a nonlocal softened pi-spin disclination structure associated with a half-quantum vortex although spin correlations are short ranged. We have also estimated fluctuation-dependent critical frequencies for half-quantum vortex nucleation in rotating optical traps. These results indicate that the strongly fluctuating ultracold spinor system is a promising candidate for studying topological orders that are the focus of many other fields.
We consider an ultracold quantum degenerate gas in an optical lattice inside a cavity. This system represents a simple but key model for “quantum optics with quantum gases,” where a quantum description of both light and atomic motion is equally important. Due to the dynamical entanglement of atomic motion and light, the measurement of light affects the many-body atomic state as well. The conditional atomic dynamics can be described using the Quantum Monte Carlo Wave Function Simulation method. In this paper, we emphasize how this usually complicated numerical procedure can be reduced to an analytical solution after some assumptions and approximations valid for macroscopic Bose-Einstein condensates (BEC) with large atom numbers. The theory can be applied for lattices with both low filling factors (e.g. one atom per lattice site in average) and very high filling factors (e.g., a BEC in a double-well potential). The purity of the resulting multipartite entangled atomic state is analyzed.
We explore the quantum dynamics of photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. Inside of an optical resonator, photoassociation of quantum degenerate atoms involves the interaction of three coupled quantum fields for the atoms, molecules, and the photons. The feedback created by a high-QQQ optical cavity causes the cavity field to become a dynamical quantity whose behavior is linked in a nonlinear manner to the atoms inside and where vacuum fluctuations have a more important role than in free space. We develop and compare several methods for calculating the dynamics of the atom-molecule conversion process with a coherently driven cavity field. We first present an alternate operator representation for the Hamiltonian from which we derive an improved form of mean field theory and an approximate solution of the Heisenberg-Langevin (HL) equations that properly accounts for quantum noise in the cavity field. It is shown that our improved mean field theory corrects several deficiencies in traditional mean field theory based on expectation values of annihilation and creation operators. Also, we show by direct comparison to numerical solutions of the density matrix equations that our approximate quantum solution of HL equations gives an accurate description of weakly or undriven cavities where mean field theories break down.
Bose-Einstein condensation has in the last two decades been observed in cold atomic gases and in solid-state physics quasiparticles, exciton-polaritons and magnons, respectively. The perhaps most widely known example of a bosonic gas, photons in blackbody radiation, however exhibits no Bose-Einstein condensation, because the particle number is not conserved and at low temperatures the photons disappear in the system’s walls instead of massively occupying the cavity ground mode. This is not the case in a small optical cavity, with a low-frequency cutoff imprinting a spectrum of photon energies restricted to values well above the thermal energy. The here reported experiments are based on a microscopic optical cavity filled with dye solution at room temperature. Recent experiments of our group observing Bose-Einstein condensation of photons in such a setup are described. Moreover, we discuss some possible applications of photon condensates to realize quantum manybody states in periodic photonic lattices and photonic Josephson devices.
The properties of phase transitions and the types of order present in the low-temperature states of matter are fundamentally dependent on the dimensionality of physical systems. Generally, highly ordered states are more robust in higher dimensions, while thermal and quantum fluctuations, which favour disordered states, play a more important role in lower dimensions. The case of a two-dimensional (2d) Bose fluid is particularly fascinating because of its "marginal" behaviour. In an infinite uniform 2d fluid thermal fluctuations at any non-zero temperature are strong enough to destroy the fully ordered state associated with Bose--Einstein condensation, but are not strong enough to suppress superfluidity in an interacting system at low, but non-zero temperatures. Further, the presence of residual "quasi-long-range" order at low temperatures leads to an interesting interplay between superfluidity and condensation in all experimentally relevant finite-size systems. In these notes we give an introduction to the physics of 2d Bose fluids from an atomic physics perspective. Our goal is to summarize the recent progress in theoretical understanding and experimental investigation of ultra-cold atomic gases confined to 2d geometry, and we also hope to provide a useful introduction to these systems for researchers working on related topics in other fields of physics.