Molecular Bose-Einstein Condensate Research Articles

Postadiabatic Hamiltonian for low-energy excitations in a slowly-time-dependent BCS-BEC crossover

We develop a Hamiltonian that describes the time-dependent formation of a molecular Bose-Einstein condensate from a Bardeen-Cooper-Schrieffer state of fermionic atoms as a result of slowly sweeping through a Feshbach resonance. In contrast to many other calculations in the field, our Hamiltonian includes the leading postadiabatic effects that arise because the crossover proceeds at a nonzero sweep rate. We apply a path-integral approach and a stationary phase approximation for the molecular $\mathbf{k}=\mathbf{0}$ background, which is a good approximation for narrow resonances [see, e.g., Diehl and Wetterich, Phys. Rev. A 73, 033615 (2006) as well as Diehl, Gies, Pawlowski, and Wetterich, Phys. Rev. A 76, 053627 (2007)]. We use two-body adiabatic approximations to solve the atomic evolution within this background. The dynamics of the $\mathbf{k}\ensuremath{\ne}\mathbf{0}$ molecular modes is solved within a dilute gas approximation and by mapping it onto a purely bosonic Hamiltonian. Our main result is a postadiabatic effective Hamiltonian in terms of the instantaneous bosonic (Anderson-)Bogoliubov modes, which holds throughout the whole resonance, as long as the Feshbach sweep is slow enough to avoid breaking Cooper pairs.

Realization of BEC-BCS-crossover physics in a compact oven-loaded magneto-optic-trap apparatus

We report on a simple oven-loaded magneto-optical trap (MOT) apparatus for the creation of both molecular Bose-Einstein condensates (mBEC) and degenerate Fermi gases (DFGs) of lithium. The apparatus does not require a Zeeman slower or a 2D MOT nor does it require any separation or differential pumping between the effusive atom source and the science chamber. The result is an exceedingly simple, inexpensive, and compact vacuum system ideal for miniaturization. We discuss our work in the context of other realizations of quantum degenerate gases by evaporation in optical dipole traps and illustrate that our apparatus meets the key requirements of atom number and trap lifetime. We also demonstrate with this system the production of a mBEC, and we use it to observe the pairing gap of a strongly interacting two-component DFG in the BEC-BCS crossover regime.

A numerical study of the ground state and dynamics of atomic–molecular Bose–Einstein condensates

In this paper, we numerically investigate the ground-state structure and dynamics of atomic–molecular Bose–Einstein condensates at zero temperature, which are modeled by coupled Gross–Pitaevskii equations (GPEs). To get the ground state, we evolve a gradient flow with discrete normalization numerically. To study the dynamics, we employ an efficient numerical method—the time-splitting Fourier pseudospectral method for solving the coupled GPEs. The proposed numerical methods have been numerically tested and employed in studying the mechanism on how an atomic condensate can be converted into an atomic–molecular mixture or a pure molecular condensate from an atomic condensate either in equilibrium or dynamically.

Precise Determination of the Structure Factor and Contact in a Unitary Fermi Gas

We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be 3.06±0.08 at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum MonteCarlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.

On the dynamics of the Fermi–Bose model

We consider the exponential matrix representing the dynamics of the Fermi–Bose model in an undepleted bosonic field approximation. A recent application of this model is molecular dimers dissociating into its atomic compounds. The problem is solved in D spatial dimensions by dividing the system matrix into blocks with generalizations of Hankel matrices, here referred to as D-block-Hankel matrices. The method is practically useful for treating large systems, i.e. dense computational grids or higher spatial dimensions, either on a single standard computer or a cluster. In particular the results can be used for studies of three-dimensional physical systems of arbitrary geometry. We illustrate the generality of our approach by giving numerical results for the dynamics of Glauber type atomic pair correlation functions for a non-isotropic three-dimensional harmonically trapped molecular Bose–Einstein condensate.

Quantum coherence establishment of Bose–Einstein condensates induced by random system dissipation

By using a weak imaginary random potential to simulate the random system dissipation and considering the quantum many-body effect, the role of random system dissipation in the quantum coherence establishment of Bose–Einstein condensates (BECs) is studied. It is found that even very weak random system dissipation may induce an obvious interference pattern between two initially independent BECs after the overlapping. Moreover, the random system dissipation has no effect on the spatial period of the interference fringes, which is identical to that observed in the current interference experiments. Under the assumption of weak dissipation, increasing the dissipation strength may accelerate the construction of the observable relative phase. Other behaviours of the interference are also investigated. The theoretical analysis and the numerical simulation show good consistency. This sort of interference has an observable effect, which significantly differs from other quantum interference mechanisms. The work may provide further theoretical basis for the future interference experiment of molecular BECs (Kohstall et al 2011 New J. Phys. 13 065027), considering the possible dissipation of the molecular BECs (e.g. the destruction of the weakly bound Feshbach molecules and the dissipation of the condensate fraction).

Macroscopic amplification of electroweak effects in molecular Bose-Einstein condensates

We investigate the possible use of Bose-Einstein condensates of diatomic molecules to measure nuclear spin-dependent parity violation effects, outlining a detection method based on the internal Josephson effect between molecular states of opposite parity. When applied to molecular condensates, the fine experimental control achieved in atomic bosonic Josephson junctions could provide data on anapole moments and neutral weak couplings.

Formation of parametric solitons in coupled atom–molecule quantum gases via controlled nonlinear interactions

We consider an atomic Bose–Einstein condensate parametrically coupled to a molecular condensate with tunable interactions. The space distribution and nonlinear dynamics of this coupled system, especially the parametric solitons, are investigated within the full parameter space accounts for all the nonlinear two-body collisions, together with the atom–molecule conversion coupling and the bare formation energy of the molecular species. The results show that the exact parametric solitons can be formed via controlled nonlinear interactions, and the atom–molecule transfer term can provide an effective potential which can be used to stable the coupled system even in the absence of the external potential. We also give an experimental setup and detection of the atomic–molecular Bose–Einstein condensates in future experiments.

Quantum phases of atomic Fermi gases with anisotropic spin-orbit coupling

We consider a general anisotropic spin-orbit coupling (SOC) and analyze the phase diagrams of both balanced and imbalanced Fermi gases for the entire BCS--Bose-Einstein condensate (BEC) evolution. In the first part, we use the self-consistent mean-field theory at zero temperature, and show that the topological structure of the ground-state phase diagrams is quite robust against the effects of anisotropy. In the second part, we go beyond the mean-field description, and investigate the effects of Gaussian fluctuations near the critical temperature. This allows us to derive the time-dependent Ginzburg-Landau theory, from which we extract the effective mass of the Cooper pairs and their critical condensation temperature in the molecular BEC limit.

Exactly solvable models for multiatomic molecular Bose–Einstein condensates

I introduce two families of exactly solvable models for multiatomic hetero-nuclear and homo-nuclear molecular Bose–Einstein condensates through the algebraic Bethe ansatz method. The conserved quantities of the respective models are also shown.

Observation of interference between two molecular Bose–Einstein condensates

We have observed the interference between two Bose–Einstein condensates of weakly bound Feshbach molecules of fermionic 6Li atoms. Two condensates are prepared in a double-well trap and, after release from this trap, overlap in expansion. We detect a clear interference pattern that unambiguously demonstrates the de Broglie wavelength of molecules. We verify that only the condensate fraction shows interference. With increasing interaction strength, the pattern vanishes because elastic collisions during overlap remove particles from the condensate wave function. For strong interaction, the condensates do not penetrate each other as they collide hydrodynamically.

Elimination of collisional effects in an R-type atom–molecule adiabatic passage

We propose an efficient scheme to avoid collision-induced dynamical instabilities in the generation of heteronuclear molecular Bose–Einstein condensates based on an R-type photoassociative adiabatic passage. This scheme allows us to completely compensate the intraspecies collisions by tunable interspecies collisions, and thereby achieve a robust atom–molecule conversion which is equivalent to that in a collision-free case. By taking the formation of stable 41K87Rb molecules as an example, we study the feasibility of the scheme.

Effect of coupling strength on atomic-to-molecular condensate conversion in Raman photoassociation

We study two-photon Raman photoassociation for creating a coherent molecular Bose-Einstein condensate (BEC) from an atomic BEC. By exploring the dynamics of the coupled system, we show that the atom-to-molecule conversion efficiency can be controlled by changing the atom-molecule coupling strength and the effective two-photon Raman detuning. Atom-molecule coupling strength and the effective two-photon Raman detuning can be controlled by changing the laser intensity. We analyze the dynamics of the coupled atom-molecular condensate system by changing the laser intensity over a broad range, keeping the effective two-photon Raman detuning fixed. The effective two-photon Raman detuning depends on the two-photon detuning, Rabi frequencies, and the light shifting (AC Stark shift) of the levels. To keep the effective two-photon Raman detuning fixed, the two-photon detuning is varied to compensate for the light shifting of levels with laser intensity. The corresponding changes in the effective decay rates and the scattering length due to the change in the Rabi frequencies have been taken into account. Dependence of the conversion efficiency on the effective two-photon Raman detuning has also been studied by varying the laser intensity over a narrow range, keeping the two-photon detuning unchanged. The dynamics of the coupled system has been studied in Gross-Pitaevskii and modified Gross-Pitaevskii approaches to demonstrate the effect of the higher order nonlinearity (Lee-Huang-Yang term) with the increase in the laser intensity.

Molecular Bose-Einstein condensation in a Bose gas with a wide Feshbach resonance at finite temperatures

Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length ${a}_{s}$ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.

Entangling the free motion of a particle pair: An experimental scenario

The concept of dissociation-time entanglement provides a means of manifesting non-classical correlations in the motional state of two counter-propagating atoms. In this article, we discuss in detail the requirements for a specific experimental implementation, which is based on the Feshbach dissociation of a molecular Bose-Einstein condensate of fermionic lithium. A sequence of two magnetic field pulses serves to delocalize both of the dissociation products into a superposition of consecutive wave packets, which are separated by a macroscopic distance. This allows to address them separately in a switched Mach-Zehnder configuration, permitting to conduct a Bell experiment with simple position measurements. We analyze the expected form of the two-particle wave function in a concrete experimental setup that uses lasers as atom guides. Assuming viable experimental parameters the setup is shown to be capable of violating a Bell inequality.

Achieving ground-state polar molecular condensates by chainwise atom-molecule adiabatic passage

We generalize the idea of chainwise stimulated Raman adiabatic passage (STIRAP) [Kuznetsova \textit{et al.} Phys. Rev. A \textbf{78}, 021402(R) (2008)] to a photoassociation-based chainwise atom-molecule system, with the goal of directly converting two-species atomic Bose-Einstein condensates (BEC) into a ground polar molecular BEC. We pay particular attention to the intermediate Raman laser fields, a control knob inaccessible to the usual three-level model. We find that an appropriate exploration of both the intermediate laser fields and the stability property of the atom-molecule STIRAP can greatly reduce the power demand on the photoassociation laser, a key concern for STIRAPs starting from free atoms due to the small Franck-Condon factor in the free-bound transition.

Atom-molecule dephasing in an SU(1,1) interferometer based on the stimulated dissociation of a molecular Bose-Einstein condensate

We propose to implement a sub-shot-noise matter-wave interferometer via the stimulated dissociation of a molecular Bose-Einstein condensate and study the collisional loss of atom-molecule coherence during its phase-acquisition time. The obtained $n$-atom states are two-atom [SU(1,1)] coherent states with number variance $\ensuremath{\Delta}n\ensuremath{\propto}n$ compared to $\ensuremath{\Delta}n\ensuremath{\propto}\sqrt{n}$ for the spin [SU(2)] coherent states formed by coherent splitting of an atomic condensate. Consequently, the Lorentzian atom-molecule phase diffusion is faster than the Gaussian phase diffusion between separated atomic condensates by a $\sqrt{n}$ factor.

Control of the dynamics of coupled atomic-molecular Bose-Einstein condensates: Modified Gross-Pitaevskii approach

We study the dynamics of the atomic and molecular Bose-Einstein condensates (BECs) of $^{87}\text{R}\text{b}$ in a spherically symmetric trap coupled by stimulated Raman photoassociation process. Considering the higher order nonlinearity in the atom-atom interaction we analyze the dynamics of the system using coupled modified Gross-Pitaevskii (MGP) equations and compare it with mean-field coupled Gross-Pitaevskii (GP) dynamics. Considerable differences in the dynamics are obtained in these two approaches at large scattering length, i.e., for large values of peak-gas parameter ${x}_{pk}\ensuremath{\ge}{10}^{\ensuremath{-}3}$. We show how the dynamics of the coupled system is affected when the atom-molecule and molecule-molecule interactions are considered together with the atom-atom interaction and also when the strengths of these three interactions are increased. The effect of detuning on the efficiency of conversion of atomic fractions into molecules is demonstrated and the feasibility of maximum molecular BEC formation by varying the Raman detuning parameter at different values of time is explored. Thus by varying the Raman detuning and the scattering length for atom-atom interaction one can control the dynamics of the coupled atomic-molecular BEC system. We have also solved coupled Gross-Pitaevskii equations for atomic to molecular condensate formation through magnetic Feshbach resonance in a BEC of $^{85}\text{R}\text{b}$. We found similar features for oscillations between atomic and molecular condensates noted in previous theoretical study and obtained fairly good agreement with the evolution of total atomic condensate observed experimentally.

Regular and irregular spin-mixing dynamics in coupled spin-1 atomic and molecular Bose-Einstein condensates

Regular and irregular spin-mixing dynamics are studied in a spin-1 atomic Bose-Einstein condensate coupled with a molecular condensate. Based on the experimental photoassociation spectroscopy of $^{87}\text{R}\text{b}$ spin-1 atoms, a two-channel model is proposed, in which two zero-spin atoms can be associated with a molecular state via a laser field, and a pair of $+1$- and $\ensuremath{-}1$-spin atoms can also be associated with the same molecular state via the same laser field. We find that the spin-mixing dynamics can be manipulated by the laser field and a magnetic field. Both regular and irregular oscillations can be observed under different parameters. Using the Fourier transform analysis, the spin-mixing dynamics may be changed from the regular oscillation with localized spectral distributions to irregular oscillation with a broad spectral distribution.

Design of Infrared Laser Pulses for the Vibrational De-excitation of Translationally Cold Li2 Molecules

In connection with attempts to form molecular Bose-Einstein condensates, there have been reports in the literature of the preparation of samples of translationally cold alkali metal dimers. The molecules in these samples are generally in excited vibrational levels. To form a stable Bose-Einstein condensate, the molecules must be de-excited to their lowest vibrational state. In this paper, we demonstrate that through the use of optimal control theory, it is possible to design a sequence of infrared laser pulses that will de-excite a sample of (7)Li2 molecules from the v = 10 vibrational level of their (1)Sigma(g)+ ground electronic state to their lowest v = 0 vibrational level with an overall efficiency of 91.1%.