In this paper, we investigate the spectrum of light scattered from a Bose-Einstein condensate in the framework of f-deformed boson. We use an f-deformed quantum model in which the Gardiners phonon operators for BEC are deformed by an operator-valued function, f(n), of the particle-number operator n. We consider the collisions between the atoms as a special kind of f-deformation. The collision rate k 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 k and eta=1/N (N, total number of condensate atoms) the scattering spectrum shows deviation from the spectrum associated with nondeformed Bose-Einstein condensate.
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.
The time-dependent correlation functions of q-deformed Bose gas are studied. We find relation of zeros of the correlation functions with the Fisher zeros of partition function of the system. Complex temperature appears as a result of q-deformation and evolution of correlation function. A particular case of q-deformed Bose particles on two levels is examined and zeros of correlation functions and Fisher zeros of partition function are analyzed.
In this paper, we investigate the propagation of a weak optical probe pulse in an f-deformed Bose- Einstein condensate (BEC) of a gas with the -type three- level atoms in the electromagnetically induced transparency (EIT) regime. We use an f- deformed generalization of an effective two- level quantum model of the three- level configuration in which the Gardiner phonon operators for BEC are deformed by an operator- valued function, f(n), of the particle- number operator n. With making use of the quantum approach of the angular momentum theory we obtain the eigenvalues and eigenfunctions of the …
In this paper, we investigate tunable control of the group velocity of a weak probe field propagating through an f-deformed Bose-Einstein condensate of three-level atoms beyond the rotating wave approximation. For this purpose, we use an f- deformed generalization of an effective two-level quantum model of the three-level configuration without the rotating wave approximation in which the Gardiners phonon operators for Bose-Einstein condensate are deformed by an operator- valued function,f(n), of the particle- number operator n . Corrections produced by the counter- rotating terms appear in the…
We show that it is possible to generate entanglement between two distant Bose-Einstein condensates by detection of Hanbury Brown-Twiss type correlations in photons Bragg-scattered by the condensates. Upon coincident detection of two photons by two detectors, the projected joint state of two condensates is shown to be non-Gaussian. We verify the existence of entanglement by showing that the partially transposed state is negative. Further we use the inequality in terms of higher order moments to confirm entanglement. Our proposed scheme can be generalized for multiple condensates and also for sp…
We show that Bose-Einstein condensate can be created in quasi-one-dimensional systems in a purely geometrical way, namely by bending or other suitable deformation of a tube.
In the recently proposed two-parameter $\tildeμ,q$-deformed Bose gas model [Ukr. J. Phys. {\bf 58}, 1171 (2013), arXiv:1312.1573] aimed to take effectively into account both compositeness of particles and their interaction, the $\tildeμ,q$-deformed virial expansion of the equation of state (EOS) was obtained. In this paper we further explore the $\tildeμ,q$-deformation, namely the version of $\tildeμ,q$-Bose gas model involving deformed distributions and correlation functions. In the model, we explicitly derive the one- and two-particle deformed distribution functions and the intercept of two-…
For the recently introduced μ-deformed analog of Bose gas model (μ-Bose gas model) we study some thermodynamical aspects. Namely, we calculate total number of particles and, from it, the deformed partition function, both involving dependence on the deformation parameter μ. Such dependence of thermodynamic functions on the μ-parameter is at the core of modification of Bose gas model and arises through the use of new techniques given by us, the μ-calculus, an alternative to the well-known q-calculus (Jackson derivative and integral). Necessary elements of μ-calculus are first presented. Then, fo…
We present a novel approach to the Bose polaron based on the notion of quantum groups, also known as $q$-deformed Lie algebras. In this approach, a mobile impurity can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath, in which the impurity is immersed. Accordingly, the Bose polaron can be described as a bath of noninteracting $q$-deformed bosons, which allows us to provide an analytical formulation of the Bose polaron at arbitrary couplings. Particularly, we derive its ground state energy in the phonon branch of the Bogoliubov dispe…
We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose-Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulation. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, th…
The Gardiner's phonon presented for a particle-number conserving approximation method to describe the dynamics of Bose-Einstein Condesation (BEC) (C.W. Gardiner, Phys. Rev. A 56, 1414 (1997)) is shown to be a physical realization of the $q$-deformed boson, which was abstractly developed in quantum group theory. On this observation, the coherent output of BEC atoms driven by a radio frequency (r.f) field is analyzed in the viewpoint of a $q$-deformed Fock space. It is illustrated that the $q$-deformation of bosonic commutation relation corresponds to the non-ideal BEC with the finite particle n…
We consider two dilute gas Bose-Einstein condensates with opposite velocities from which a monochromatic light field detuned far from the resonance of the optical transition is coherently scattered. In the thermodynamic limit, when the relative fluctuations of the atom number difference between the two condensates vanish, the relative phase between the Bose-Einstein condensates may be established in a superposition state by detections of spontaneously scattered photons, even though the condensates have initially well-defined atom numbers. For a finite system, stochastic simulations show that t…
We consider the deformed Bose gas model with the deformation structure function that is the combination of a q-deformation and a quadratically polynomial deformation. Such a choice of the unifying deformation structure function enables us to describe the interacting gas of composite (two-fermionic or two-bosonic) bosons. Using the relevant generalization of the Jackson derivative, we derive a two-parametric expression for the total number of particles, from which the deformed virial expansion of the equation of state is obtained. The latter is interpreted as the virial expansion for the effect…
Symmetric Tamm-Dancoff (STD) type $q$-deformed quantum oscillators are used as the base for constructing the respective STD type $q$-Bose gas model. In this letter, within the STD $q$-deformed Bose gas model we derive explicit analytic expressions for the $r$-particle momentum distribution functions, and for the (momentum) correlation function intercepts of 2nd, 3rd, and any $r$th order. Besides, we obtain large-momentum asymptotic formulas for the $r$th order intercepts which show dependence on the $q$-parameter only. The obtained formulas provide new example, in addition to already known two…
In the study of many-particle systems both the interaction of particles can be essential and such feature as their internal (composite) structure. To describe these aspects, the theory of deformed oscillators is very efficient. Viewing the particles as p,q-deformed bosons, in the corresponding p,q-Bose gas model we obtain in explicit form virial expansion along with the 2nd to 5th virial coefficients. The obtained virial coefficients depend on the deformation parameters p,q in the form symmetric under p<->q, and at p->1, q->1 turn into those known for usual bosons. Besides real parameters, we …
We consider excitons in a quantum dot as q-deformed systems. Interaction of some excitonic systems with one cavity mode is considered. Dynamics of the system is obtained by diagonalizing total Hamiltonian and emission spectrum of quantum dot is derived. Physical consequences of q-deformed exciton on emission spectrum of quantum dot is given. It is shown that when the exciton system deviates from Bose statistics, emission spectra will become multi peak. With our investigation we try to find the origin of the q-deformation of exciton. The optical response of excitons, which affected by the nonli…
Recently, the deformed μ-Bose gas model based on so called μ-deformed oscillators was proposed. For that model, the intercepts of r-particle momentum correlation functions (correlation functions at coinciding momenta of particles) were treated for r=2,3, within certain order of approximation in μ. In this work, we derive for μ-Bose gas model the {\it exact} expressions for r-particle correlation function intercepts, for all r, through Lerch transcendent and find their asymptotics (as functions of μ). For 2-, 3-particle intercepts and deformed distribution function <a^†_k a_k> the dependence on…
We propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor $F=1$ Bose-Einstein condensate residing in an optical lattice. We characterize the complete experimental procedure--- the local operations, the measurements and the inequality---necessary to run the Bell test. We show how the degree of violation of the Bell inequality depends on the strengths of the two-body correlations and on the number of scattered pairs. We show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. …
It is well known that in the presence of a ring cavity the light scattering from a uniform atomic ensemble can become unstable resulting in the collective atomic recoil lasing. This is the result of a positive feedback due to the cavity. We propose to add an additional electronic feedback loop based on the photodetection of the scattered light. The advantage is a great flexibility in choosing the feedback algorithm, since manipulations with electric signals are very well developed. In this paper we address the application of such a feedback to atoms in the Bose-Einstein condensed state and exp…
The second-order coherence of photons scattered from a trapped Bose-Einstein condensate is found to be enhanced for the scattering angles that are either the same or symmetrical with respect to the direction of laser propagation. The enhancement occurs periodically with respect to the time interval between photons, and becomes less and less pronounced with increasing the strength of the interaction between atoms.
Low energy elastic scattering between clouds of Bose condensed atoms leads to the well known s-wave halo with atoms emerging in all directions from the collision zone. In this paper we discuss the emergence of Hanbury Brown and Twiss coincidences between atoms scattered in nearly parallel directions. We develop a simple model that explains the observations in terms of an interference involving two pairs of atoms each associated with the elementary s wave scattering process.
The so-called μ-deformed oscillator (or μ-oscillator) introduced by A.Jannussis, though possesses rather exotic properties with respect to other better known deformed oscillator models, also has good potential for diverse physical applications. In this paper, the corresponding μ-Bose gas model based on μ-oscillators is explored. Within this model, the intercepts λ^(2)(K) and λ^(3)(K) of two- and three-particle momentum correlation functions are calculated with the goal of possible application for modeling the non-Bose type behavior of the intercepts of two- and three-pion correlations, observe…
We establish the relation of the second virial coefficient of certain $(\tildeμ,q)$-deformed Bose gas model, recently proposed by the authors in [Ukr. J. Phys., 2013], to the interaction and compositeness parameters when either of these factors is taken into account separately. When the interaction is dealt with, the deformation parameter becomes linked directly to the scattering length, and the effective radius of interaction (in general, to scattering phases). The additionally arising temperature dependence is a new feature absent in the deformed Bose gas model within adopted interpretation …
A pulsed atom laser derived from a Bose-Einstein condensate is used to probe a second target condensate. The target condensate scatters the incident atom laser pulse. From the spatial distribution of scattered atoms, one can infer important properties of the target condensate and its interaction with the probe pulse. As an example, we measure the s-wave scattering length that, in low energy collisions, describes the interaction between the |F=1,m_F=-1> and |F=2,m_F=0> hyperfine ground states in 87Rb.
A method to create paired atom laser beams from a metastable helium atom laser via four-wave mixing is demonstrated. Radio frequency outcoupling is used to extract atoms from a Bose Einstein condensate near the center of the condensate and initiate scattering between trapped and untrapped atoms. The unequal strengths of the interactions for different internal states allows an energy-momentum resonance which leads to the creation of pairs of atoms scattered from the zero-velocity condensate. The resulting scattered beams are well separated from the main atom laser in the 2-dimensional transvers…
We investigate the dynamics of matter and optical waves at the early stage of superradiant Rayleigh scattering from Bose-Einstein Condensates. Our analysis is within a spatially dependent quantum model which is capable of providing analytic solutions for the operators of interest. The predictions of the present model are compared to the predictions of a closely related mean field model, and we provide a procedure that allows one to calculate quantum expectation values by averaging over semiclassical solutions. The coherence properties of the outgoing scattered light are also analyzed, and it i…
We study a protocol for constructing a squeezed atom laser for a model originating from the generalized uncertainty principle. We show that the squeezing effects arising from such systems do not require any squeezed light as an input, but the squeezing appears automatically because of the structure of the model it owns. The output atom laser beam becomes squeezed due to the nonlinear interaction between the Bose-Einstein condensate and the deformed radiation field created due to the noncommutative structure. We analyze several standard squeezing techniques based on the analytical expressions f…
We propose a new formulation for atomic side mode dynamics from super-radiant light scattering of trapped atoms. A detailed analysis of the recently observed super-radiant light scattering from trapped bose gases [S. Inouye {\it et al.}, Science {\bf 285}, 571 (1999)] is presented. We find that scattered light intensity can exhibit both oscillatory and exponential growth behaviors depending on densities, pump pulse characteristics, temperatures, and geometric shapes of trapped gas samples. The total photon scattering rate as well as the accompanied matter wave amplification depends explicitly …
We study cavity quantum electrodynamics of Bose-condensed atoms that are subjected to continuous monitoring of the light leaking out of the cavity. Due to a given detection record of each stochastic realization, individual runs spontaneously break the symmetry of the spatial profile of the atom cloud and this symmetry can be restored by considering ensemble averages over many realizations. We show that the cavity optomechanical excitations of the condensate can be engineered to target specific collective modes. This is achieved by exploiting the spatial structure and symmetries of the collecti…
We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved detector. For the case of photons, phase matching conditions completely define the final state of the system, and in the case of two colliding BECs, simple analogy implies a spherical momentum distribution of scattered atoms. We find, however, that the final momenta of the scattered atoms instead lie on an ellipsoid whose radii are smaller th…
Collisions of Bose-Einstein condensates can be used as a mean to generate correlated pairs of atoms. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within Bo…
When a laser beam passes through a rotating ground glass (RGG), the scattered light exhibits thermal statistics. This is extensively used in speckle imaging. This scattering process has not been addressed in photon picture and is especially relevant if non-classical light is scattered by the RGG. We develop the photon picture for the scattering process using the Bose statistics for distributing $N$ photons in $M$ pixels. We obtain analytical form for the P-distribution of the output field in terms of the P-distribution of the input field. In particular we obtain a general relation for the $n$-…
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in an…
Off-resonant optical imaging is the most popular method for continuous monitoring of a Bose-Einstein condensate (BEC). However, the disturbance caused by scattered photons places a serious limitation on the lifetime of such continuously-monitored condensates. In this paper, we demonstrate that a new choice of feedback control can overcome the heating effects of the measurement backaction. In particular, we show that the measurement backaction caused by off-resonant optical imaging is a multimode quantum-field effect, as the entire heating process is not seen in single-particle or mean-field mo…
We study the scattering of a weak and far-detuned light from a system of ultracold bosons in 1D and 3D optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott insulator phases of the Bose gas in a lattice, and we analyze in detail how the scattering depends on …
The Bose distribution for a gas of nonrelativistic free bosons is derived in the framework of $qp$-deformed second quantization. Some thermodynamical functions for such a system in D dimensions are derived. Bose-Einstein condensation is discussed in terms of the parameters q and p as well as a parameter $ν_0'$ which characterizes the representation space of the oscillator algebra.
Both classical and quantum dynamics of the synchronization between two nonlinear mechanical modes scattered from Bose-Einstein condensates (BECs) by the standing-wave laser beam are comparatively investigated. As the ultra-low dissipations of the momentum modes in the atomic BECs, the synchronized dynamics are studied in a framework of closed-system theory in order to track down both the classical and the quantum synchronizations from an angle of quantum control. The classical synchronization and the relevant dynamics of measure synchronization, the quantum synchronization and two different ty…
In this paper we study nonequilibrium dynamics of one dimensional Bose gas from the general perspective of dynamics of integrable systems. After outlining and critically reviewing methods based on inverse scattering transform, intertwining operators, q-deformed objects, and extended dynamical conformal symmetry, we focus on the form-factor based approach. Motivated by possible applications in nonlinear quantum optics and experiments with ultracold atoms, we concentrate on the regime of strong repulsive interactions. We consider dynamical evolution starting from two initial states: a condensate…
Quantum and q-deformed algebras find their application not only in mathematical physics and field theoretical context, but also in phenomenology of particle properties. We describe (i) the use of quantum algebras U_q(su_n) corresponding to Lie algebras of the groups SU(n), taken for flavor symmetries of hadrons, in deriving new high-accuracy hadron mass sum rules, and (ii) the use of (multimode) q-oscillator algebras along with q-Bose gas picture in modelling the properties of the intercept λof two-pion (two-kaon) correlations in heavy-ion collisions, as λshows sizable observed deviation from …
