The spectrum of light scattered from a Bose–Einstein condensate is studied in the limit of particle-number conservation. To this end, a description in terms of deformed bosons is invoked and this leads to a deviation from the usual predict spectrum’s shape as soon as the number of particles decreases. PACS number(s): 03.65.Fd (Algebraic methods), 03.75.Fi (Bose condensation), 42.50.Ct (Quantum statistical description of interaction of light and matter) 1 The recent achievements of Bose–Einstein condensate (BEC) with a gas of atoms confined by a magnetic trap [1] has stimulated renewed interest in the question as to what signatures Bose–Einstein condensation imprints in the spectrum of light scattered from atoms in such a condensate [2, 3]. As well known, to deal with the dynamics of BEC gas the Bogolubov approximation in quantum many-body theory [4] is an efficient approach, in which the creation
The spectrum of light scattered from a Bose–Einstein condensate is studied in the limit of particle-number conservation. To this end, a description in terms of deformed bosons is invoked and this leads to a deviation from the usual predict spectrum’s shape as soon as the number of particles decreases. PACS number(s): 03.65.Fd (Algebraic methods), 03.75.Fi (Bose condensation), 42.50.Ct (Quantum statistical description of interaction of light and matter) 1 The recent achievements of Bose–Einstein condensate (BEC) with a gas of atoms confined by a magnetic trap [1] has stimulated renewed interest in the question as to what signatures Bose–Einstein condensation imprints in the spectrum of light scattered from atoms in such a condensate [2, 3]. As well known, to deal with the dynamics of BEC gas the Bogolubov approximation in quantum many-body theory [4] is an efficient approach, in which the creation
In this paper, we investigate the spectrum of light scattered from a Bose-Einstein condensate in the framework of -deformed boson.We use an -deformed quantum model in which the Gardiner's phonon operators for BEC are deformed by an operator-valued function,, of the particle-number operator n .We consider the collisions between the atoms as a special kind of -deformation.The collision rateκ is regarded as the deformation parameter and the spectrum of light scattered from the deformed BEC is analyzed.In particular, we find that with increasing the values of deformation parameters κ and N 1 = η ( , total number of condensate atoms) the scattering spectrum shows deviation from the spectrum associated with nondeformed Bose-Einstein condensate.
The first successful experimental realization of a Bose-Einstein condensate (BEC) in 1995 sparked a still growing research activity that in the meantime has led to beautiful and surprising results, such as the interference of matter waves [4], the Mott-superfluid phase transition [49] or the direct observation of Anderson localization of matter waves [10]. The strong interest in BECs arises, among others, from the possibility to investigate known but hard to study quantum systems on a rather macroscopic scale: for example one can load ultra-cold bosons into an optical lattice created by a standing light wave, and thereby simulate a solid state device. When it comes to a measurement on the BEC, however, essentially all measurement techniques result in the destruction of the condensate: for example in the so called “time of flight method” the optical lattice is switched off to observe the expansion of the trapped atoms and thereby directly visualize their momentum distribution, which highlights the condensed component [11]. In this thesis we elaborate on a means to probe a Bose-Einstein condensate from outside, with a scattering particle. The interaction between the probe particle and the bosons allows energy exchange between them, i.e., this setup includes inelastic scattering. After the scattering process, the condensate is still confined in the optical lattice and can therefore be used for further investigations. Of course, this method of probing a BEC is only then a serious alternative if the properties of the BEC can be inferred from the scattering signal. Besides outlining the scattering formalism, the central aim of this work is to show how the properties of the BEC can be deduced from those quantities accessible in a scattering experiment, like for example the transmission or the inelastic cross section. The other, equally strong motivation of this work concerns the signature of the interaction between the bosons in the scattering quantities. The dynamics of an analog classical system depends strongly on the interaction strength, which can induce a complex structure of the underlying phase space like, e.g., the appearance of a separatrix or even the emergence of chaotic dynamics in a globally mixed regular-chaotic phase space. We are interested to which extent such phase-space metamorphosis is reflected in the properties of the scattering particle. Currently light scattering (Bragg spectroscopy) on an optical lattice [78, 77] or rather on an optical lattice embedded into a cavity [62,68,19] is under intense investigation. These efforts predominantly aim at a characterization of the Mott-superfluid transition by specific scattering properties. In the present thesis we focus on condensates loaded in two and three lattice sites, with a large number of bosons. These systems exhibit a diversity of important physical effects (as we will see below) and thus are of paradigmatic relevance for a detailed understanding of multiparticle quantum dynamics in periodic potentials.
The q -deformed Bose–Einstein distribution derived from the q -boson algebra is used to study the low-temperature behavior of an ideal q -deformed Bose gas with relativistic energy spectrum. The effects of q -deformation on the properties relative to Bose–Einstein condensation (BEC) are discussed. It is shown that q -deformation leads to some novel characteristics different from those of an original Bose gas, which include the criteria on the occurrence of BEC, critical temperature and jump of heat capacity at the critical point. The results obtained here provide a unified description for the properties of q -deformed Bose systems from the nonrelativistic case to the ultrarelativistic limit, so that some important conclusions in the literature are included in this paper.
We have observed strong scattering of a probe light by dilute Bose–Einstein condensate (BEC) 87 Rb gas in a tight magnetic trap. The scattering light forms fringes at the image plane. It is found that we can infer the real size of the condensation and the number of the atoms by modelling the imaging system. We present a quantitative calculation of light scattering by the condensed atoms. The calculation shows that the experimental results agree well with the prediction of the generalized diffraction theory, and thus we can directly observe the phase transition of BEC in a tight trap.
We review recent experiments on the Bose-Einstein condensation of photons in a dye-filled optical microresonator. The most well-known example of a photon gas, photons in blackbody radiation, does not show Bose-Einstein condensation. Instead of massively populating the cavity ground mode, photons vanish in the cavity walls when they are cooled down. The situation is different in an ultrashort optical cavity imprinting a low-frequency cutoff on the photon energy spectrum that is well above the thermal energy. The latter allows for a thermalization process in which both temperature and photon number can be tuned independently of each other or, correspondingly, for a nonvanishing photon chemical potential. We here describe experiments demonstrating the fluorescence-induced thermalization and Bose-Einstein condensation of a two-dimensional photon gas in the dye microcavity. Moreover, recent measurements on the photon statistics of the condensate, showing Bose-Einstein condensation in the grand-canonical ensemble limit, will be reviewed. Introduction Quantum statistical effects become relevant when a gas of particles is cooled, or its density is increased, to the point where the associated de Broglie wavepackets spatially overlap. For particles with integer spin (bosons), the phenomenon of Bose-Einstein condensation (BEC) then leads to macroscopic occupation of a single quantum state at finite temperatures [1]. Bose-Einstein condensation in the gaseous case was first achieved in 1995 by laser and subsequent evaporative cooling of a dilute cloud of alkali atoms [2, 3, 4], as detailed in Chapter 3 of this volume. The condensate atoms can be described by a macroscopic singleparticle wavefunction, similar to the case of liquid helium [1]. Bose-Einstein condensation has also been observed for exciton-polaritons, which are hybrid states of matter and light [5, 6, 7] (see Chapter 4), magnons [8] (see Chapter 25), and other physical systems. Other than material particles, photons usually do not show Bose-Einstein condensation [9]. In blackbody radiation, the most common Bose gas, photons at low temperature disappear, instead of condensing to a macroscopically occupied ground-state mode. In this system, photons have a vanishing chemical potential, meaning that the number of photons is determined by the available thermal energy and cannot be tuned independently from temperature.
The quantum nonlinear dynamics of an atomic Bose-Einstein condensate (BEC) in a double-well potential is studied. Using a double-well single-particle potential model system and a two-mode approximation, results showed that the coherent oscillations resulting from tunneling are suppressed when the number of atoms is greater than a critical value. The spectrum if nonresonant light scattered by the condensate to include an asymmetric double peak structure with peak separation and relative heights determined by the number of atoms in the condensate and the interaction strength for hard sphere collisions.