Degenerate Atoms Research Articles

Quantum dynamics of cavity-assisted photoassociation of Bose-Einstein-condensed atoms

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-Q 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 introduce 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/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.

Teleporting N-qubit unknown atomic state by utilizing the V-type three-level atom

Realizing the teleportation of quantum state, especially the teleportation of N-qubit quantum state, is of great importance in quantum information. In this paper, Raman-interaction of the V-type degenerate three-level atom and single-mode cavity field is studied by utilizing complete quantum theory. Then a new scheme for teleporting N-qubit unknown atomic state via Raman-interaction of the V-type degenerate three-level atom with a single-mode cavity field is proposed, which is based upon the complete quantum theory mentioned above.

Pump-probe spectroscopy in degenerate two-level atoms with arbitrarily strong fields

We study the pump and probe absorption spectra, as a function of the probe detuning, in a degenerate two-level atomic system, for the case where the probe intensity is high enough to affect the pump absorption. The theory is valid for any ${F}_{g}\ensuremath{\rightarrow}{F}_{e}$ alkali-metal transition interacting with an arbitrarily intense pump and probe (with general Rabi frequencies ${\ensuremath{\Omega}}_{1,2}$) which are perpendicularly polarized with either ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ or $\ensuremath{\pi}$ polarization. We have constructed a computer program that can calculate the spectra without requiring one to write out the Bloch equations explicitly. We show that, when the pump is ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ polarized and the probe $\ensuremath{\pi}$ polarized, or vice versa, the pump and probe absorptions depend on the Zeeman coherences between the nearest-neighboring ground or excited Zeeman sublevels, whereas when the pump is ${\ensuremath{\sigma}}_{+}$ polarized and the probe ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized, or vice versa, the Zeeman coherences that directly determine the absorption are between next-nearest neighbors. We report calculations of the pump and probe absorption spectra for the cycling ${F}_{g}=2\ensuremath{\rightarrow}{F}_{e}=3$ transition in the ${D}_{2}$ line of $^{87}\text{R}\text{b}$, interacting with a resonant ${\ensuremath{\sigma}}_{+}$-polarized pump and either a $\ensuremath{\pi}$- or a ${\ensuremath{\sigma}}_{\ensuremath{-}}$- polarized probe. The probe and pump absorption spectra are analyzed by considering the contributions that derive from the individual ${m}_{g}\ensuremath{\rightarrow}{m}_{e}$ transitions. We then show how these contributions depend on the ground- and excited-state populations and Zeeman coherences, and investigate the role played by transfer of coherence from the excited to the ground hyperfine state. We show that the pump and probe absorption spectra are mirror images of each other when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}>\ensuremath{\Gamma}$, and have the same behavior at line center and complementary behavior in the wings, when ${\ensuremath{\Omega}}_{1}\ensuremath{\ge}{\ensuremath{\Omega}}_{2}<\ensuremath{\Gamma}$ ($\ensuremath{\Gamma}$ is the rate of spontaneous decay from ${F}_{e}$ to ${F}_{g}$).

Coherent mesoscopic quantum tunneling in boson-fermion mixtures

We show that cold atom systems of simultaneously trapped Bose-Einstein condensates (BECs) and quantum degenerate fermionic atoms provide promising laboratories for the study of macroscopic quantum tunneling. Our theoretical studies reveal that the spatial extent of a small trapped BEC immersed in a Fermi sea can tunnel and coherently oscillate between the values of the separated and mixed configurations (the phases of the phase separation transition of BEC-fermion systems). We evaluate the period, amplitude, and dissipation rate for $^{23}\mathrm{Na}$ and $^{40}\mathrm{K}$ atoms, and we discuss the experimental prospects for observing this phenomenon.

Absorption spectrum of a resonantly driven degenerate V-type atom with a dc-field coupling between excited states

We study the absorption spectra of a degenerate V-type atom, where a resonant driving field and a probe field drive different branches of transitions and a dc field is applied to drive the transition between two excited states. The effects of vacuum induced coherence (VIC) on the absorption spectra are investigated. It is demonstrated that in some special cases the VIC can lead to the depression of absorption and narrow resonance. The origin of these features are discussed. When the pump field and the dc field have the same intensity, it is interesting to find that the whole absorption spectrum comes mainly from the absorptions induced by the interferences among different transitions between dressed states.

Ultrafast and Ultraslow Oxygen Atom Transfer Reactions between Late Metal Centers

Oxotrimesityliridium(V), (mes)3Ir=O (mes = 2,4,6-trimethylphenyl), and trimesityliridium(III), (mes)3Ir, undergo extremely rapid degenerate intermetal oxygen atom transfer at room temperature. At low temperatures, the two complexes conproportionate to form (mes)3Ir-O-Ir(mes)3, the 2,6-dimethylphenyl analogue of which has been characterized crystallographically. Variable-temperature NMR measurements of the rate of dissociation of the mu-oxo dimer combined with measurements of the conproportionation equilibrium by low-temperature optical spectroscopy indicate that oxygen atom exchange between iridium(V) and iridium(III) occurs with a rate constant, extrapolated to 20 degrees C, of 5 x 107 M-1 s-1. The oxotris(imido)osmium(VIII) complex (ArN)3Os=O (Ar = 2,6-diisopropylphenyl) also undergoes degenerate intermetal atom transfer to its deoxy partner, (ArN)3Os. However, despite the fact that its metal-oxygen bond strength and reactivity toward triphenylphosphine are nearly identical to those of (mes)3Ir=O, the osmium complex (ArN)3Os=O transfers its oxygen atom 12 orders of magnitude more slowly to (ArN)3Os than (mes)3Ir=O does to (mes)3Ir (kOsOs = 1.8 x 10-5 M-1 s-1 at 20 degrees C). Iridium-osmium cross-exchange takes place at an intermediate rate, in quantitative agreement with a Marcus-type cross relation. The enormous difference between the iridium-iridium and osmium-osmium exchange rates can be rationalized by an analogue of the inner-sphere reorganization energy. Both Ir(III) and Ir(V) are pyramidal and can form pyramidal iridium(IV) with little energetic cost in an orbitally allowed linear approach. Conversely, pyramidalization of the planar tris(imido)osmium(VI) fragment requires placing a pair of electrons in an antibonding orbital. The unique propensity of (mes)3Ir=O to undergo intermetal oxygen atom transfer allows it to serve as an activator of dioxygen in cocatalyzed oxidations, for example, acting with osmium tetroxide to catalyze the aerobic dihydroxylation of monosubstituted olefins and selective oxidation of allyl and benzyl alcohols.

Quantum entanglement manifestation of transition to nonlinear self-trapping for Bose-Einstein condensates in a symmetric double well

We investigate the nonlinear self-trapping phenomenon of the Bose-Einstein condensates (BEC) in a symmetric double-well, emphasizing on its behind dynamical phase transition. With increasing the nonlinear parameter depicting the interaction between the degenerate atoms the BEC turns to be self-trapped manifesting an asymmetric distribution of the atomic density profile. Essence of this phenomenon is revealed to be a continuous phase transition and underlying critical behavior is studied analytically and found to follow a logarithm scaling-law. We then go beyond the mean field treatment and extend to discuss the effect of the many-body quantum fluctuation on the transition. It is found that the transition point is shifted and the scaling-law is broken. In particular, the quantum phase transition is accompanied by the change of the entanglement entropy which is found to reach maximum at transition point. Behind physics is revealed.

Continuous-measurement-enhanced self-trapping of degenerate ultracold atoms in a double well: Nonlinear quantum Zeno effect

In the present paper we investigate the influence of measurements on the quantum dynamics of degenerate Bose atoms gases in a symmetric double-well. We show that continuous measurements enhance asymmetry on the density distribution of the atoms and broaden the parameter regime for self-trapping. We term this phenomenon as nonlinear quantum Zeno effect in analog to the celebrated Zeno effect in a linear quantum system. Under discontinuous measurements, the self-trapping due to the atomic interaction in the degenerate bosons is shown to be destroyed completely. Underlying physics is revealed and possible experimental realization is discussed.

Collapse mechanism of the condensate wavefunction in the Bose-Fermi mixture with attraction between the components

The ground state of the mixture of degenerate Bose and Fermi atoms in a trap has been analyzed on the basis of the effective Hamiltonian. The two types of the solutions of the modified Gross-Pitaevskii equation that correspond to the stationary and unstable states of the Bose gas have been found numerically. The chemical potential and energy are found as functions of the number of bosons for these two types of the solutions. The manyvalued character of these functions has been analyzed and the critical number of bosons at which the system collapse occurs has been determined.

Implementing the Deutsch–Jozsa algorithm by using Schrödinger cat states in cavity QED

We propose a scheme to implement the Deutsch–Jozsa algorithm by using Schrödinger cat states in cavity quantum electron-dynamics (QED). The scheme is based on the Raman interaction of a degenerate three-level Λ-type atom with a coherent state in a cavity. By using Schrödinger cat states, the atomic spontaneous emission can be minimized and the Hadamard transformation in our scheme is not needed.

Hybrid apparatus for Bose-Einstein condensation and cavity quantum electrodynamics: Single atom detection in quantum degenerate gases

We present and characterize an experimental system in which we achieve the integration of an ultrahigh finesse optical cavity with a Bose-Einstein condensate (BEC). The conceptually novel design of the apparatus for the production of BECs features nested vacuum chambers and an in vacuo magnetic transport configuration. It grants large scale spatial access to the BEC for samples and probes via a modular and exchangeable “science platform.” We are able to produce Rb87 condensates of 5×106 atoms and to output couple continuous atom lasers. The cavity is mounted on the science platform on top of a vibration isolation system. The optical cavity works in the strong coupling regime of cavity quantum electrodynamics and serves as a quantum optical detector for single atoms. This system enables us to study atom optics on a single particle level and to further develop the field of quantum atom optics. We describe the technological modules and the operation of the combined BEC cavity apparatus. Its performance is characterized by single atom detection measurements for thermal and quantum degenerate atomic beams. The atom laser provides a fast and controllable supply of atoms coupling with the cavity mode and allows for an efficient study of atom field interactions in the strong coupling regime. Moreover, the high detection efficiency for quantum degenerate atoms distinguishes the cavity as a sensitive and weakly invasive probe for cold atomic clouds.

Dissipation of System and Atom in Two-Photon Jaynes–Cummings Model with Degenerate Atomic Levels

The method of perturbative expansion of master equation is employed to study the dissipative properties of system and of atom in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels. The numerical results show that the degeneracy of atomic levels prolongs the period of entanglement between the atom and the field. The asymptotic value of atomic linear entropy is apparently increased by the degeneration. The amplitude of local entanglement and disentanglement is suppressed. The better the initial coherence property of the degenerate atom, the larger the coherence loss.

Preparing Fock states of the electromagnetic field via Raman interaction

A recent proposal creating Fock states of the quantized radiation field, of kind | 2 N 〉 , was presented. The scheme was based on dispersive interaction of a cavity field with two-level Rydberg atoms. Here we get the same, via a simplified scheme using Raman interaction of the cavity field with degenerate three-level atoms.

Feshbach-Resonant Interactions inK40andLi6Degenerate Fermi Gases

We theoretically examine a system of Fermi degenerate atoms coupled to bosonic molecules by a Feshbach resonance, focusing on the superfluid transition to a molecular Bose-Einstein condensate dressed by Cooper pairs of atoms. This problem raises interest because it is unclear at present whether bimodal density distributions observed recently in 40K and 6Li are due to a condensate of bosonic molecules or fermionic atom pairs. As opposed to 40K, we find that any measurable fraction of above-threshold bosonic molecules is necessarily absent for the 6Li system in question, which strongly implicates Cooper pairs as the culprit behind its bimodal distributions.

Entropy squeezing of the field interacting with a nearly degenerate V-type three-level atom

The position- and momentum-entopic squeezing properties of the optical field in the system of a nearly degenerate three-level atom interacting with a single-mode field are investigated. Calculation results indicate that when the field is initially in the vacuum state, it may lead to squeezing of the position entropy or the momentum entropy of the field if the atom is prepared properly. The effects of initial atomic state and the splitting of the excited levels of the atom on field entropies are discussed in this case. When the initial field is in a coherent state, we find that position-entropy squeezing of the field is present even if the atom is prepared in the ground state. By comparing the variance squeezing and entropy squeezing of the field we confirm that entropy is more sensitive than variance in measuring quantum fluctuations.

Microtraps and Atom Chips: Toolboxes for Cold Atom Physics

Magnetic microtraps and Atom Chips are safe, small-scale, reliable and flexible tools to prepare ultra-cold and degenerate atom clouds as sources for various atom-optical experiments. We present an overview of the possibilities of the devices and indicate how a microtrap can be used to prepare and launch a Bose-Einstein condensate for use in an atom clock or an interferometer.

Generation of superposed phase states via Raman interaction

A recent proposal producing superpositions of two truncated phase states in a high-Q microwave cavity has been presented. The scheme was based on dispersive interactions of two-level Rydberg atoms with a single mode field inside a cavity. Here we consider a simplified scheme doing the same, via Raman interaction of the field with degenerate three-level atoms. The extension to 2K phase states components (K>1) is discussed.

Controlled hole burning in the Fock space via Raman interaction

A recent proposal creating states of the quantized radiation field, with controlled holes in their photon number distribution, was presented [Phys. Lett. A290 (2001) 234]. The scheme was based on dispersive interaction of a cavity field with two-level Rydberg atoms. Here we consider a simpler scheme doing the same, via Raman interaction of the cavity field with degenerate three-level atoms.

Effects of a thermal reservoir on variational functions in open systems

We connect the theory of a Lyapunov functional for an open system with the thermophysical concept of the relative entropy or equivalently with the entropy production rate. In order to do this we consider the environment of the open system as a thermal reservoir, which introduces the temperature as a thermophysical quantity. The general theory of the Lyapunov functional of an open system constructs a metric operator which contains an element of ambiguity in its scaling. This ambiguity can be removed by assuming a thermostatistic environment which fixes the scaling of the metric operator in a unique manner. The Lyapunov functional thus acquires a thermophysical meaning and can be connected with a relative entropy. In this case the metric operator is related to the inverse of the stationary density operator of the system. We illustrate the theory on a two-level atomic system and a degenerate three-level atom which are exposed to a thermal electromagnetic environment.

Coupling constants for a degenerate Fermi gas confined to a quasi-one-dimensionalharmonic trap

A theory for the coupling constants between spin-polarized degenerate fermionic atoms isdeveloped for the case of atoms confined to a quasi-one-dimensional harmonic trap.Exploiting the presence of the Fermi edge and the large number of fermions, it is shownthat the resulting effective one-dimensional interaction can be parametrized by three sets ofinteraction coefficients, two for forward scattering and one for backward scattering. In thecase of identical fermions, backscattering dominates, because the contact part of theeffective one-dimensional interaction must be subtracted. Analytic expressions forthe interaction coefficients for the effective contact interaction, which is relevantfor the inter-component interactions, and for the ‘p-wave’ interaction appearingin next order, are given. As an example, we calculate and discuss in detail theeffective coupling constants for the marginally long ranged dipole–dipole interaction.