Alternative method for exact diagonalization of the Hamiltonian describing a two-level system coupled to a bose gas with an Einstein spectrum

A simple method is described which exactly diagonalizes the Hamiltonian describing a two-level system coupled to a Bose gas with an Einstein spectrum. The method is based on a separation of the boson field into two mutually orthogonal (and commuting) parts, one of which corresponds to the bound spectrum, the other corresponds to the continuous spectrum. It is also shown that such an additive, linear, field-splitting method is inadequate for the case of a nonconstant spectrum.     

Relaxation of a single two-level system

A relaxation problem for a single two-level system coupled to a Bose field is investigated. The stationary state and relaxation time of the system is analysed. The correction to the unperturbed stationary state is derived in the fourth order of the interaction between the system and bosons. The criteria for an application of the perturbation calculation are discussed.Supported in part by the Polish Academy of Sciences under Contract No. MR I-9.The author would like to express his sincere thanks to the members of the Department of Theoretical Physics at the Silesian University for their comments and discussions.     

Relaxation of the ideal Bose gas

For the ideal Bose gas we study the approach to equilibrium. Above the critical temperature we prove exponential behaviour, with a relaxation time of the order (T-T _c)^-2 around T _c. For T _c we find the t ^-1 law for the two-point function.     

The dynamics of three coupled dipolar Bose Einstein condensates

The dynamics of the three coupled dipolar Bose–Einstein condensates containing N bosons is investigated within a mean-field semiclassical picture based on the coherent-state method. Varieties of periodic solutions （configured as vortex, single depleted well, and dimerlike states） are obtained analytically when the fixed points are identified on the N=constant. The system dynamics are studied via numeric integration of trimer motion equations, thus revealing macroscopic effects of population inversion and self-trapping with different initial states. In particular, the trajectory of the oscillations of the populations in each well shows how the dynamics of the condensates are effected by the presence of dipole–dipole interaction and gauge field.     

Decoherence in a two-level system coupled to a fermion environment with phase transitions

The decoherence process characterized by Loschmidt echo (LE) in a two-level system dephasingly coupled to a fermion environment with phase transitions is studied in this Letter. The results show that the LE of the two-level system may act as a witness of the environment's phase transitions, which is similar to the relation between quantum phase transitions and the LE.     

Spin orbit coupled Bose Einstein condensate in a two dimensional bichromatic optical lattice

We numerically investigate the localization of Bose Einstein condensate (BEC) with spin orbit coupling in a two dimensional bichromatic optical lattice. We study localization in weakly interacting and non-interacting regimes. The existence of stationary localized states in the presence of spin–orbit and Rabi couplings has been confirmed. We find that spin orbit coupling favors localization, whereas Rabi coupling has a slight delocalization effect.     

Optomechanically induced transparency with Bose Einstein condensate in double-cavity optomechanical system

We propose a novel technique of generating multiple optomechanically induced transparency(OMIT) of a weak probe field in hybrid optomechanical system. This system consists of a cigar-shaped Bose–Einstein condensate(BEC), trapped inside each high finesse Fabry-Pérot cavity. In the resolved sideband regime, the analytic solutions of the absorption and the dispersion spectrum are given. The tunneling strength of the two resonators and the coupling parameters of the each BEC in combination with the cavity field have the appearance of three distinct OMIT windows in the absorption spectrum.Furthermore, whether there is BEC in each cavity is a key factor in the number of OMIT windows determination. The technique presented may have potential applications in quantum engineering and quantum information networks.     

Dynamics of a two-level system coupled to Ohmic bath: a perturbation approach

The quantum dynamics, both non-equilibrium and equilibrium, of the dissipative two-level system is studied by means of the perturbation approach based on a unitary transformation. It works well for the whole parameter range and and our main results are: the coherence-incoherence transition is at ; for the non-equilibrium correlation ; the susceptibility is of a double peak structure for and the Shibas relation is exactly satisfied; at the transition point the equilibrium correlation in the long time limit.Received: 14 October 2003, Published online: 8 June 2004PACS: 72.20.Dp General theory, scattering mechanisms - 05.30.-d Quantum statistical mechanics     

Production of a chromium Bose–Einstein condensate

The recent achievement of Bose–Einstein condensation of chromium atoms [1] has opened longed-for experimental access to a degenerate quantum gas with long-range and anisotropic interaction. Due to the large magnetic moment of chromium atoms of 6 μ_B, in contrast to other Bose–Einstein condensates (BECs), magnetic dipole-dipole interaction plays an important role in a chromium BEC. Many new physical properties of degenerate gases arising from these magnetic forces have been predicted in the past and can now be studied experimentally. Besides these phenomena, the large dipole moment leads to a breakdown of standard methods for the creation of a chromium BEC. Cooling and trapping methods had to be adapted to the special electronic structure of chromium to reach the regime of quantum degeneracy. Some of them apply generally to gases with large dipolar forces. We present here a detailed discussion of the experimental techniques which are used to create a chromium BEC and allow us to produce pure condensates with up to 10⁵ atoms in an optical dipole trap. We also describe the methods used to determine the trapping parameters.     

Dynamics of a quantum oscillator strongly and off-resonantly coupled with a two-level system

Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time scale, the quantum oscillator shows collapses, revivals and fractional revivals, which are encountered in oscillator observables like the mean number of oscillator quanta and in the two-level inversion population. Also the scattered oscillator field shows doublets with symmetrically displaced peaks.     

Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system

We show that two-photon transport is strongly correlated in one-dimensional waveguide coupled to a two-level system. The exact S matrix is constructed using a generalized Bethe-ansatz technique. We show that the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.     

Bose condensate drag in a system of two coupled traps

A system of two plane traps disposed one above the other and confined atomic Bose condensate is considered. The possibility of entraining atoms of one of the traps by the atoms of the other trap upon the rotation of the latter is studied. The average angular momentum induced by the rotation of the first trap is found for the atoms in the second trap.     

Bose–Einstein condensation of lithium

7 Li has been studied in a magnetically trapped gas. Many-body quantum theory predicts that the occupation number of the condensate is limited to about 1400 atoms because of the effectively attractive interactions between ⁷Li atoms. Using a versitile phase-contrast imaging technique, we experimentally observe the condensate number to be consistent with this limit. We discuss our measurements, the current theoretical understanding of BEC in a gas with attractive interactions, and future experiments we hope to perform. Received: 4 June 1997     

Dynamics of a two-level system coupled to a quantum oscillator: transformed rotating-wave approximation

For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but still keeps the simple mathematical structure of the ordinary rotating-wave approximation. We have calculated the energy levels of ground and lower-lying excited states, as well as the time-dependent quantum dynamics. It is obvious that the approach is quite simple and can be easily extended to more complicated situation. Besides, the results are compared with the numerically exact ones to show that for weak to intermediate coupling and moderate detuning our analytic calculations are quantitatively in good agreement with the exact ones.     

Dynamics of quantum Fisher information in a two-level system coupled to multiple bosonic reservoirs

We consider the optimal parameter estimation for a two-level system coupled to multiple bosonic reservoirs. By using quantum Fisher information(QFI), we investigate the effect of the Markovian reservoirs' number N on QFI in both weak and strong coupling regimes for a two-level system surrounded by N zero-temperature reservoirs of field modes initially in the vacua. The results show that the dynamics of QFI non-monotonically decays to zero with revival oscillations at some time in the weak coupling regime depending on the reservoirs' parameters. Furthermore, we also present the relations between the QFI flow, the flows of energy and information, and the sign of the decay rate to gain insight into the physical processes characterizing the dynamics.     

Phase-modulated quadrature squeezing in two coupled cavities containing a two-level system

The phase-modulated quadrature squeezing in the system that composed of two coupled cavities interacting with a two-level atom is investigated. The variances of the amplitude and phase quadrature of the output field are calculated.It turns out that the squeezing behaviors of the output field can be obviously modified due to the phase difference of the coupling strengths between the atom and the two cavities. The squeezing in one quadrature(i.e., phase quadrature) can be transferred into another(i.e., amplitude quadrature), or the quadrature squeezing located at the low-frequency region can be transferred into the high-frequency region by modulating the relative phase of the coupling strengths. Furthermore, the effects of the decay mismatch between the two cavities and the coupling mismatch between the atom and the cavities on the quadrature squeezing have been discussed. The results show that both the decay mismatch and the coupling mismatch play a positive role in generating better quadrature squeezing.     

Stability of coherent states of a Bose gas of two-level atoms in resonant laser field at zero temperature

It is shown that a two-level atom Bose gas in a strong resonant laser field at zero temperature is a mixture of two condensates with a certain density ratio. The stability criteria for stationary states of such a system relative to the increase in the amplitudes of quasi-Bogolyubov elementary excitations of the Bose gas are formulated. It is shown that, in addition to conventional acoustic mode, a mode gap exists with a gap proportional to the laser field amplitude. Under certain conditions, deviations from ideality of the gas may lead to instability and decomposition of the condensate.