Formation of quantum-degenerate sodium molecules

Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model

We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate for both atoms-to-molecule pairing and molecular dissociation processes. We find that for the latter process with a linear energy dispersion of atomic modes, the emerging phase can have a thermalized energy distribution of noninteracting bosons with the temperature defined by the rate of the transition. This provides a simple interpretation of the phase transition in terms of the creation of equilibrium Bose-Einstein condensate.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

Dynamical Phase Transitions in Sampling Complexity

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (ACM Press, New York, New York, USA, 2011), p. 333]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular, and optical systems.

Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity

The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning.

Multidiscontinuity algorithm for world-line Monte Carlo simulations

We introduce a multidiscontinuity algorithm for the efficient global update of world-line configurations in Monte Carlo simulations of interacting quantum systems. This algorithm is a generalization of the two-discontinuity algorithms introduced in Refs. [N. Prokof'ev, B. Svistunov, and I. Tupitsyn, Phys. Lett. A 238, 253 (1998)] and [O. F. Syljuåsen and A. W. Sandvik, Phys. Rev. E 66, 046701 (2002)]. This generalization is particularly effective for studying Bose-Einstein condensates (BECs) of composite particles. In particular, we demonstrate the utility of the generalized algorithm by simulating a Hamiltonian for an S=1 antiferromagnet with strong uniaxial single-ion anisotropy. The multidiscontinuity algorithm not only solves the freezing problem that arises in this limit, but also allows the efficient computing of the off-diagonal correlator that characterizes a BEC of composite particles.

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%.

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Ultracold triplet molecules in the rovibrational ground state

We report here on the production of an ultracold gas of tightly bound Rb2 triplet molecules in the rovibrational ground state, close to quantum degeneracy. This is achieved by optically transferring weakly bound Rb2 molecules to the absolute lowest level of the ground triplet potential with a transfer efficiency of about 90%. The transfer takes place in a 3D optical lattice which traps a sizeable fraction of the tightly bound molecules with a lifetime exceeding 200 ms.

Collisional properties of p-wave Feshbach molecules

We have observed p-wave Feshbach molecules for all three combinations of the two lowest hyperfine spin states of 6Li. By creating a pure molecular sample in an optical trap, we measured the inelastic collision rates of p-wave molecules. We have also measured the elastic collision rate from the thermalization rate of a breathing mode which was excited spontaneously upon molecular formation.

Total control over ultracold interactions via electric and magnetic fields

The scattering length is commonly used to characterize the strength of ultracold atomic interactions, since it is the leading parameter in the low-energy expansion of the scattering phase shift. Its value can be modified via a magnetic field, by using a Feshbach resonance. However, the effective range term, which is the second parameter in the phase shift expansion, determines the width of the resonance and gives rise to important properties of ultracold gases. Independent control over this parameter is not possible by using a magnetic field only. We demonstrate that a combination of magnetic and electric fields can be used to get independent control over both parameters, which leads to full control over elastic ultracold interactions.

Interactions and dynamics in Li+Li2 ultracold collisions

A potential energy surface for the lowest quartet electronic state ((4)A(')) of lithium trimer is developed and used to study spin-polarized Li+Li(2) collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of Li(2). Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states, the cross sections are only quite weakly dependent on details of the potential energy surface.

Atom-molecule Rabi oscillations in a Mott insulator

We observe large-amplitude Rabi oscillations between an atomic and a molecular state near a Feshbach resonance. The experiment uses 87Rb in an optical lattice and a Feshbach resonance near 414 G. The frequency and amplitude of the oscillations depend on the magnetic field in a way that is well described by a two-level model. The observed density dependence of the oscillation frequency agrees with theoretical expectations. We confirmed that the state produced after a half-cycle contains exactly one molecule at each lattice site. In addition, we show that, for energies in a gap of the lattice band structure, the molecules cannot dissociate.

Ultracold heteronuclear molecules in a 3D optical lattice

We report on the creation of ultracold heteronuclear molecules assembled from fermionic 40K and bosonic 87Rb atoms in a 3D optical lattice. Molecules are produced at a heteronuclear Feshbach resonance on both the attractive and the repulsive sides of the resonance. We precisely determine the binding energy of the heteronuclear molecules from rf spectroscopy across the Feshbach resonance. We characterize the lifetime of the molecular sample as a function of magnetic field and measure lifetimes between 20 and 120 ms. The efficiency of molecule creation via rf association is measured and is found to decrease as expected for more deeply bound molecules.

Repulsively bound atom pairs in an optical lattice

Throughout physics, stable composite objects are usually formed by way of attractive forces, which allow the constituents to lower their energy by binding together. Repulsive forces separate particles in free space. However, in a structured environment such as a periodic potential and in the absence of dissipation, stable composite objects can exist even for repulsive interactions. Here we report the observation of such an exotic bound state, which comprises a pair of ultracold rubidium atoms in an optical lattice. Consistent with our theoretical analysis, these repulsively bound pairs exhibit long lifetimes, even under conditions when they collide with one another. Signatures of the pairs are also recognized in the characteristic momentum distribution and through spectroscopic measurements. There is no analogue in traditional condensed matter systems of such repulsively bound pairs, owing to the presence of strong decay channels. Our results exemplify the strong correspondence between the optical lattice physics of ultracold bosonic atoms and the Bose-Hubbard model-a link that is vital for future applications of these systems to the study of strongly correlated condensed matter and to quantum information.

Pseudopotential analog for zero-range photoassociation and Feshbach resonance

A zero-range approach to atom-molecule coupling is developed in analogy to the Fermi-Huang pseudopotential approach to collisions. It is shown by explicit comparison to an exactly solvable finite-range model that replacing the molecular bound-state wave function with a regularized delta function can reproduce the exact scattering amplitude in the long-wavelength limit. Using this approach, we find an analytical solution to the two-channel Feshbach resonance problem for two atoms in a spherical harmonic trap, highlighting the strong dependence of the effective scattering length and bare-molecule population on the atom-molecule coupling strength.

Long-lived Feshbach molecules in a three-dimensional optical lattice

We have created and trapped a pure sample of Feshbach molecules in a three-dimensional optical lattice. Compared to previous experiments without a lattice, we find dramatic improvements such as long lifetimes of up to 700 ms and a near unit efficiency for converting tightly confined atom pairs into molecules. The lattice shields the trapped molecules from collisions and, thus, overcomes the problem of inelastic decay by vibrational quenching. Furthermore, we have developed an advanced purification scheme that removes residual atoms, resulting in a lattice in which individual sites are either empty or filled with a single molecule in the vibrational ground state of the lattice.

Ultracold molecule production via a resonant oscillating magnetic field

A novel atom-molecule conversion technique has been investigated. Ultracold 85Rb atoms sitting in a dc magnetic field near the 155 G Feshbach resonance are associated by applying a small sinusoidal oscillation to the magnetic field. There is resonant atom to molecule conversion when the modulation frequency closely matches the molecular binding energy. We observe that the atom to molecule conversion efficiency depends strongly on the frequency, amplitude, and duration of the applied modulation and on the phase space density of the sample. This technique offers high conversion efficiencies without the necessity of crossing or closely approaching the Feshbach resonance and allows precise spectroscopic measurements. Efficiencies of 55% have been observed for pure Bose-Einstein condensates.

Quantum-degenerate mixture of fermionic lithium and bosonic rubidium gases

We report on the observation of sympathetic cooling of a cloud of fermionic 6Li atoms which are thermally coupled to evaporatively cooled bosonic 87Rb. Using this technique we obtain a mixture of quantum-degenerate gases, where the Rb cloud is colder than the critical temperature for Bose-Einstein condensation and the Li cloud is colder than the Fermi temperature. From measurements of the thermalization velocity we estimate the interspecies s-wave triplet scattering length |amx|=20(+9)(-6)aB. We found that the presence of residual rubidium atoms in the |2, 1> and the |1, -1> Zeeman substates gives rise to important losses due to inelastic collisions.

Einstein-Podolsky-Rosen correlations via dissociation of a molecular Bose-Einstein condensate

Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstrate that strongly entangled atomic beams may be produced which possess Einstein-Podolsky-Rosen (EPR) correlations in field quadratures in direct analogy to the position and momentum correlations originally considered by EPR.

Quantum phases in a resonantly interacting boson-fermion mixture

We consider a resonantly interacting boson-fermion mixture of 40K and 87Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for 40K and 87Rb atoms, and 40K-87Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.

Confinement induced molecules in a 1D Fermi gas

We have observed two-particle bound states of atoms confined in a one-dimensional matter waveguide. These bound states exist irrespective of the sign of the scattering length, contrary to the situation in free space. Using radio-frequency spectroscopy we have measured the binding energy of these dimers as a function of the scattering length and confinement and find good agreement with theory. The strongly interacting one-dimensional Fermi gas which we create in an optical lattice represents a realization of a tunable Luttinger liquid.

Creating ground state molecules with optical feshbach resonances in tight traps

We propose to create ultracold ground state molecules in an atomic Bose-Einstein condensate by adiabatic crossing of an optical Feshbach resonance. We envision a scheme where the laser intensity and possibly also frequency are linearly ramped over the resonance. Our calculations for (87)Rb show that for sufficiently tight traps it is possible to avoid spontaneous emission while retaining adiabaticity, and conversion efficiencies of up to 50% can be expected.

Production efficiency of ultracold feshbach molecules in bosonic and fermionic systems

We investigate the production efficiency of ultracold molecules in bosonic 85Rb and fermionic 40K when the magnetic field is swept across a Feshbach resonance. For adiabatic sweeps of the magnetic field, our novel model shows that the conversion efficiency of both species is solely determined by the phase space density of the atomic cloud, in contrast with a number of theoretical predictions. In the nonadiabatic regime our measurements of the 85Rb molecule conversion efficiency follow a Landau-Zener model.

Observation of Feshbach-like resonances in collisions between ultracold molecules

We observe magnetically tuned collision resonances for ultracold Cs2 molecules stored in a CO2-laser trap. By magnetically levitating the molecules against gravity, we precisely measure their magnetic moment. We find an avoided level crossing which allows us to transfer the molecules into another state. In the new state, two Feshbach-like collision resonances show up as strong inelastic loss features. We interpret these resonances as being induced by Cs4 bound states near the molecular scattering continuum. The tunability of the interactions between molecules opens up novel applications such as controlled chemical reactions and synthesis of ultracold complex molecules.

Coherent molecular optics using ultracold sodium dimers

Coherent molecular optics is performed using two-photon Bragg scattering. Molecules were produced by sweeping an atomic Bose-Einstein condensate through a Feshbach resonance. The spectral width of the molecular Bragg resonance corresponded to an instantaneous temperature of 20 nK, indicating that atomic coherence was transferred directly to the molecules. An autocorrelating interference technique was used to observe the quadratic spatial dependence of the phase of an expanding molecular cloud. Finally, atoms initially prepared in two momentum states were observed to cross pair with one another, forming molecules in a third momentum state. This process is analogous to sum-frequency generation in optics.

Spontaneous dissociation of 85Rb Feshbach molecules

The spontaneous dissociation of 85Rb dimers in the highest lying vibrational level has been observed in the vicinity of the Feshbach resonance that was used to produce them. The molecular lifetime shows a strong dependence on magnetic field, varying by 3 orders of magnitude between 155.5 G and 162.2 G. Our measurements are in good agreement with theoretical predictions in which molecular dissociation is driven by inelastic spin relaxation. Molecule lifetimes of tens of milliseconds can be achieved within approximately a 1 G wide region directly above the Feshbach resonance.

Molecular production in two component atomic fermi gases

We provide a practical approach to the molecular production via linear downward sweeps of Feshbach resonances in degenerate Fermi gases containing incoherent mixtures of two atomic spin states. We show that the efficiency of the association of atoms is determined just by the Landau-Zener parameter in addition to the density of the gas. Our approach of pairwise summation of the microscopic binary transition probabilities leads to an intuitive explanation for the observed saturation of the molecular production and recovers all atomic loss curves of Regal et al. [Nature (London) 427, 47 (2003))]] as well as Strecker et al. [Phys. Rev. Lett. 91, 080406 (2003))]] without adjustable parameters.

Creating a stable molecular condensate using a generalized Raman adiabatic passage scheme

We study the Feshbach resonance assisted stimulated adiabatic passage of an effective coupling field for creating stable molecules from an atomic Bose condensate. By exploring the properties of the coherent population trapping state, we show that, contrary to the previous belief, mean-field shifts need not limit the conversion efficiency as long as one chooses an adiabatic passage route that compensates the collision mean-field phase shifts and avoids the dynamical unstable regime.

Observation of heteronuclear Feshbach resonances in a mixture of bosons and fermions

Three magnetic-field induced heteronuclear Feshbach resonances were identified in collisions between bosonic 87Rb and fermionic 40K atoms in their absolute ground states. Strong inelastic loss from an optically trapped mixture was observed at the resonance positions of 492, 512, and 543+/-2 G. The magnetic-field locations of these resonances place a tight constraint on the triplet and singlet cross-species scattering lengths, yielding (-281+/-15)a(0) and (-54+/-12)a(0), respectively. The width of the loss feature at 543 G is 3.7+/-1.5 G wide; this broad Feshbach resonance should enable experimental control of the interspecies interactions.

Molecular matter-wave amplifier

We describe a matter-wave amplifier for vibrational ground-state molecules which uses a Feshbach resonance to first form quasibound molecules starting from an atomic Bose-Einstein condensate. The quasibound molecules are then driven into their stable vibrational ground state via a two-photon Raman transition inside an optical cavity. The transition from the quasibound state to the electronically excited state is driven by a classical field. Amplification of ground state molecules is then achieved by using a strongly damped cavity mode for the transition from the electronically excited molecules to the molecular ground state.

Three-boson problem near a narrow Feshbach resonance

We consider a three-boson system with resonant binary interactions and show that for sufficiently narrow resonances three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.

Observation of Feshbach resonances between two different atomic species

We have observed three Feshbach resonances in collisions between 6Li and 23Na atoms. The resonances were identified as narrow loss features when the magnetic field was varied. The molecular states causing these resonances have been identified, and additional 6Li-23Na resonances are predicted. These resonances will allow the study of degenerate Bose-Fermi mixtures with adjustable interactions and could be used to generate ultracold heteronuclear molecules.

State selective production of molecules in optical lattices

We demonstrate quantum control over both internal and external quantum degrees of freedom in a high number of identical "chemical reactions," carried out in an array of microtraps in a 3D optical lattice. Starting from a Mott insulating phase of an ultracold atomic quantum gas, we use two-photon Raman transitions to create molecules on lattice sites occupied by two atoms. In the atom-molecule conversion process, we can control both the internal rovibronic and external center of mass quantum state of the molecules. The lattice isolates the microscopic chemical reactions from each other, thereby allowing photoassociation spectra without collisional broadening even at high densities of up to 2 x 10(15) cm(-3).

Exactly solvable models for atom-molecule Hamiltonians

We present a family of exactly solvable generalizations of the Jaynes-Cummings model involving the interaction of an ensemble of SU(2) or SU(1,1) quasispins with a single boson field. They are obtained from the trigonometric Richardson-Gaudin models by replacing one of the SU(2) or SU(1,1) degrees of freedom by an ideal boson. The application to a system of bosonic atoms and molecules is reported.

Quantum phase transition in an atomic bose gas with a feshbach resonance

We show that in an atomic Bose gas near a Feshbach resonance a quantum phase transition occurs between a phase with only a molecular Bose-Einstein condensate and a phase with both an atomic and a molecular Bose-Einstein condensate. We show that the transition is characterized by an Ising order parameter. We also determine the phase diagram of the gas as a function of magnetic field and temperature: the quantum critical point extends into a line of finite temperature Ising transitions.

Dissociation and decay of ultracold sodium molecules

The dissociation of ultracold molecules was studied by ramping an external magnetic field through a Feshbach resonance. The observed dissociation energies directly yielded the strength of the atom-molecule coupling. They showed nonlinear dependence on the ramp speed. This was explained by a Wigner threshold law which predicts that the decay rate of the molecules above threshold increases with the density of states. In addition, inelastic molecule-molecule and molecule-atom collisions were characterized.

Production and state-selective detection of ultracold RbCs molecules

Using resonance-enhanced two-photon ionization, we detect ultracold, metastable RbCs molecules formed in their lowest triplet state a (3)Sigma(+) via photoassociation in a laser-cooled mixture of 85Rb and 133Cs atoms. We obtain extensive bound-bound excitation spectra of these molecules, which provide detailed information about their vibrational distribution, as well as spectroscopic data on several RbCs molecular states including a (3)Sigma(+), (2) (3)Sigma(+), and (1) (1)Pi. Analysis of this data allows us to predict strong transitions from observed levels to the absolute vibronic ground state of RbCs, potentially allowing the production of stable, ultracold polar molecules at rates in excess of 10(6) s(-1).

Observation of Bose-Einstein condensation of molecules

We have observed Bose-Einstein condensation of molecules. When a spin mixture of fermionic 6Li atoms was evaporatively cooled in an optical dipole trap near a Feshbach resonance, the atomic gas was converted into 6Li2 molecules. Below 600 nK, a Bose-Einstein condensate of up to 900 000 molecules was identified by the sudden onset of a bimodal density distribution. This condensate realizes the limit of tightly bound fermion pairs in the crossover between BCS superfluidity and Bose-Einstein condensation.

Emergence of a molecular Bose–Einstein condensate from a Fermi gas

The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen-Cooper-Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose-Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose-Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS-BEC continuum.