We study the matter-wave bistability in coupled atom-molecule quantum gases, in which heteronuclear molecules are created via an interspecies Feshbach resonance involving either two-species Bose or two-species Fermi atoms at zero temperature. We show that the resonant two-channel Bose model is equivalent to the nondegenerate parametric down-conversion in quantum optics, while the corresponding Fermi model can be mapped to a quantum optics model that describes a single-mode laser field interacting with an ensemble of inhomogeneously broadened two-level atoms. Using these analogy and the fact that both models are subject to the Kerr nonlinearity due to the two-body s-wave collisions, we show that under proper conditions, the population in the molecular state in both models can be made to change with the Feshbach detuning in a bistable fashion.
A coupled atom-molecule condensate with an intraspecies Feshbach resonance is employed to explore matter wave bistability both in the presence and in the absence of a unidirectional optical ring cavity. In particular, a set of conditions are derived that allow the threshold for bistability, due both to two-body s-wave scatterings and to cavity-mediated two-body interactions, to be determined analytically. The latter bistability is found to support, not only transitions between a mixed (atom-molecule) state and a pure molecular state as in the former bistability, but also transitions between tw…
We study the dissociation of Feshbach molecules in ultracold Fermi gases with spin-orbit (SO) coupling. Since SO coupling can induce quantum transition between the Feshbach molecules and the fully polarized Fermi gas, the Feshbach molecules can be dissociated by the SO coupling. We experimentally realized this new type of dissociation in ultracold gases of 40K atoms with SO coupling created by Raman beams, and observed that the dissociation rate is highly non-monotonic on both the positive and negative Raman-detuning sides. Our results show that the dissociation of Feshbach molecules can be co…
We study non-equilibrium dynamics of ultracold two-component Fermi gases in low-dimensional geometries after the interactions are quenched from weakly interacting to strongly interacting regime. We develop a T-matrix formalism that takes into account the interplay between Pauli blocking and tight confinement in low-dimensional geometries. We employ our formalism to study the formation of molecules in quasi-two-dimensional Fermi gases near Feshbach resonance and show that the rate at which molecules form depends strongly on the transverse confinement. Furthermore, Pauli blocking gives rise to a…
The field of ultracold quantum matter has burgeoned over the last few decades, thanks to the growing capabilities for atomic systems to be probed and manipulated with exquisite control. Researchers can now precisely create and study quantum many-body states that are effectively isolated from the external environment. Much of the work in ultracold matter has focused on systems of alkali or alkaline-earth atoms, mainly due to their ease of cooling. Extending this precise control to molecules has seen rapidly increasing interest and activity, as molecules possess additional degrees of freedom tha…
We study the non-equiliribium dynamics of atom-molecule Bose gases in a double-well potential. In this system, the internal atom-molecule tunneling has significant influence on the dynamics. We investigate the periodicity of dynamics by studying the level statistics of the quantum system. We find that chaotic energy eigenstates arise from the competition between the interwell and the atom-molecule internal tunnelings. Furthermore, we show that the physical quantities relax to the microcanonical averages in the full-quantum dynamics when the system is chaotic. This thermalization is caused by t…
We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction $D/r^3$ favors an equilateral triangular arrangement of the molecules, which competes against the square symmetry of the underlying optical lattice with lattice constant $b$ and amplitude $V$. We find the minimal-energy states at the commensurate density $n = 1/b^2$ and establish the complete square-to-triangular transformation pathway of the lattice with decreasing $V$ involving period-doubled, solitonic, and distorted-triangular conf…
We investigate theoretically radio-frequency spectroscopy of weakly bound molecules in an ultracold spin-orbit-coupled atomic Fermi gas. We consider two cases with either equal Rashba and Dresselhaus coupling or pure Rashba coupling. The former system has been realized very recently at Shanxi University [Wang et al., arXiv:1204.1887] and MIT [Cheuk et al., arXiv:1205.3483]. We predict realistic radio-frequency signals for revealing the unique properties of anisotropic molecules formed by spin-orbit coupling.
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driv…
We consider the ground state of a single "spin-down" impurity atom interacting attractively with a "spin-up" atomic Fermi gas. By constructing variational wave functions for polarons, molecules and trimers, we perform a detailed study of the transitions between each of these dressed bound states as a function of mass ratio $r=m_\uparrow/m_\downarrow$ and interaction strength. We find that the presence of a Fermi sea enhances the stability of the $p$-wave trimer, which can be viewed as a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) molecule that has bound an additional majority atom. For sufficientl…
We construct a fully self-consistent Hartree-Fock-Bogoliubov theory that describes a spinless Fermi gas with long-range interaction. We apply this theory to a system of uniform dipolar fermionic polar molecules, which has attracted much attention recently, due to rapid experimental progress in achieving such systems. By calculating the anisotropic superfluid order parameter, and the critical temperature $T_{c}$, we show that, "hign $T_c$" superfluid can be achieved with a quite modest value of interaction strength for polar molecules. In addition, we also show that the presence of the Fock exc…
We show that the excitation of long-range Rydberg molecules in a three-dimensional optical lattice can be used as a position- and time-sensitive probe of the site occupancy in the system. To this end, we detect the ions which are continuously generated by the decay of the formed Rydberg molecules. While a superfluid gas shows molecule formation for all parameters, a Mott insulator with $n=1$ filling reveals a strong suppression of the number of formed molecules. In the limit of weak probing, the technique can be used to probe the superfluid to Mott-insulator transition in real-time. Our method…
A recent experimental realization of quantum degenerate gas of $^{40}$K$^{87}$Rb molecules opens up prospects of exploring strong dipolar Fermi gases and many-body phenomena arising in that regime. Here we derive a mean-field variational approach based on the Wigner function for the description of ground-state properties of such systems. We show that the stability of dipolar fermions in a general harmonic trap is universal as it only depends on the trap aspect ratios and the dipoles' orientation. We calculate the species-independent stability diagram and the deformation of the Fermi surface (F…
We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the …
We compute the fraction of closed-channel molecules in trapped atomic Fermi gases, over the entire range of accessible fields and temperatures. We use a two-channel model of BCS--Bose-Einstein condensation (BEC) crossover theory at general temperature $T$, and show that this fraction provides a measure of the $T$ dependent pairing gap. Our calculations, containing no free parameters, are in good quantitative agreement with recent low $T$ measurements in $^6$Li. We present readily testable predictions for the dependencies of the closed-channel fraction on temperature and Fermi momentum.
In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions, the so-called Fermi polaron problem. On one side, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides quantitatively reliable insight into the phase diagram of strongly interacting population imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to study itinerant ferromagnetism, a long standing problem in quantum mechanics.
We report on the creation of ultracold gases of bosonic Feshbach molecules of NaCs. The molecules are associated from overlapping gases of Na and Cs using a Feshbach resonance at 864.12(5) G. We characterize the Feshbach resonance using bound state spectroscopy, in conjunction with a coupled-channel calculation. By varying the temperature and atom numbers of the initial atomic mixtures, we demonstrate the association of NaCs gases over a wide dynamic range of molecule numbers and temperatures, reaching 70 nK for our coldest systems and a phase-space density near 0.1. This is an important stepp…
Based on the recently developed interaction renormalization for the one-dimensional $p$-wave interaction, we study the problem of a single impurity immersed in a highly polarized Fermi sea. They interact through a narrow $p$-wave Feshbach resonance, so the effective range $r_{0}$ naturally appears in the system. We use the variational approach limited to single-particle-hole excitations on top of the unperturbed Fermi sea. The polaron exhibits two branches of solutions, namely, the attractive and repulsive branches, with varying scattering length across the resonance. We calculate the energy s…
We consider dipolar interactions between heteronuclear molecules in a low-dimensional setup consisting of two one-dimensional tubes. We demonstrate that attraction between molecules in different tubes can overcome intratube repulsion and complexes with several molecules in the same tube are stable. In situ detection schemes of the few-body complexes are proposed. We discuss extensions to the case of many tubes and layers, and outline the implications of our results on many-body physics.
The superfluid phases in the resonant dipolar Fermi gases are investigated by the standard mean-field theory. In contrast to the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid in the Fermi gases with the isotropic interactions, the resonant dipolar interaction leads to two completely different BEC phases of the tight-binding Fermi molecules on both sides of the resonance, which are characterized by two order parameters with the distinct internal symmetries. We point that near the resonance, the two competitive phases can coexist, and an emergent r…
Fermi gas of polar molecules in the Pauli-blocked regime
JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado（科罗拉多大学物理系与美国国家标准技术研究院JILA联合研究所）；ITAMP, Center for Astrophysics | Harvard & Smithsonian（哈佛-史密森尼天体物理中心）；California Institute of Technology（加州理工学院）
First-order phase transition in atom-molecule quantum degenerate mixtures with coherent three-body recombination
Missouri University of Science and Technology（密苏里科技大学）；Ben-Gurion University of the Negev（内盖夫本古里安大学）；Harvard & Smithsonian（哈佛大学与史密森尼学会）；University of Chicago（芝加哥大学）
Point defects in self-assembled crystals, such as vacancies and interstitials, attract each other and form stable clusters. This leads to a phase separation between perfect crystalline structures and defect conglomerates at low temperatures. We propose a method that allows one to tune the effective interactions between point defects from attractive to repulsive by means of external periodic fields. In the quantum regime, this allows one to engineer strongly-correlated many-body phases. We exemplify the microscopic mechanism by considering dipolar quantum gases of ground state polar molecules a…
Fermionic superfluidity in atomic Fermi gases across a Feshbach resonance is normally described by the atom-molecule theory, which treats the closed channel as a noninteracting point boson. In this work we present a theoretical description of the resonant superfluidity in analogy to the two-band superconductors. We employ the underlying two-channel scattering model of Feshbach resonance where the closed channel is treated as a composite boson with binding energy $\varepsilon_0$ and the resonance is triggered by the microscopic interchannel coupling $U_{12}$. The binding energy $\varepsilon_0$ …
We investigate magnetoassociation of ultracold fermionic Feshbach molecules in a mixture of $^{40}$K and $^{87}$Rb atoms, where we can create as many as $7\times 10^4$ $^{40}$K$^{87}$Rb molecules with a conversion efficiency as high as 45%. In the perturbative regime, we find that the conversion efficiency depends linearly on the density overlap of the two gases, with a slope that matches a parameter-free model that uses only the atom masses and the known Feshbach resonance parameters. In the saturated regime, we find that the maximum number of Feshbach molecules depends on the atoms' phase-sp…
We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moment but possessing a significant value of electric quadrupole moment. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and h…
We present a systematic theoretical study of the BCS-BEC crossover in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC). By solving the exact two-body problem in the presence of an attractive short-range interaction we show that the SOC enhances the formation of the bound state: the binding energy $E_{\text B}$ and effective mass $m_{\text B}$ of the bound state grows along with the increase of the SOC. For the many-body problem, even at weak attraction, a dilute Fermi gas can evolve from a BCS superfluid state to a Bose condensation of molecules when the SOC becomes comparable…
Ultracold polar molecules, with their long-range electric dipolar interactions, offer a unique platform for studying correlated quantum many-body phenomena such as quantum magnetism. However, realizing a highly degenerate quantum gas of molecules with a low entropy per particle has been an outstanding experimental challenge. In this paper, we report the synthesis of a low entropy molecular quantum gas by creating molecules at individual sites of a three-dimensional optical lattice that is initially loaded from a low entropy mixture of K and Rb quantum gases. We make use of the quantum statisti…
In this paper, we explore the nature of three-dimensional Bose gases at large positive scattering lengths via resummation of dominating processes involving a minimum number of virtual atoms. We focus on the energetics of the nearly fermionized Bose gases beyond the usual dilute limit. We also find that an onset instability sets in at a critical scattering length, beyond which the near-resonance Bose gases become strongly coupled to molecules and lose the metastability. Near the point of instability, the chemical potential reaches a maximum, and the effect of the three-body forces can be estima…
We investigate phase separation of Bose-Einstein condensates (BECs) of two-component atoms and one-component molecules with a homonuclear Feshbach resonance. We develop a full model for dilute atomic and molecular gases including correlation of the Feshbach resonance and all kinds of interparticle interactions, and numerically calculate order parameters of the BECs in spherical harmonic oscillator traps at zero temperature with the Bogoliubov's classical field approximation. As a result, we find out that the Feshbach resonance can induce two types of phase separation. The actual phase structur…
This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, domin…
While many-particle entanglement can be found in natural solids and strongly interacting atomic and molecular gases, generating highly entangled states between weakly interacting particles in a controlled and scalable way presents a significant challenge. We describe here a one-step method to generate entanglement in a dilute gas of cold polar molecules. For molecules in optical traps separated by a few micrometers, we show that maximally entangled states can be created using the strong off-resonant pulses that are routinely used in molecular alignment experiments. We show that the resulting a…
Molecules are the building blocks of matter and their control is key to the investigation of new quantum phases, where rich degrees of freedom can be used to encode information and strong interactions can be precisely tuned. Inelastic losses in molecular collisions, however, have greatly hampered the engineering of low-entropy molecular systems. So far, the only quantum degenerate gas of molecules has been created via association of two highly degenerate atomic gases. Here, we use an external electric field along with optical lattice confinement to create a two-dimensional (2D) Fermi gas of sp…
In several settings of physics and chemistry one has to deal with molecules interacting with some kind of an external environment, be it a gas, a solution, or a crystal surface. Understanding molecular processes in the presence of such a many-particle bath is inherently challenging, and usually requires large-scale numerical computations. Here, we present an alternative approach to the problem - that based on the notion of the angulon quasiparticle. We show that molecules rotating inside superfluid helium nanodroplets and Bose-Einstein Condensates form angulons, and therefore can be described …
Advances in light shaping for optical trapping of neutral particles have led to the development of box traps for ultracold atoms and molecules. These traps have allowed the creation of homogeneous quantum gases and opened new possibilities for studies of many-body physics. They simplify the interpretation of experimental results, provide more direct connections with theory, and in some cases allow qualitatively new, hitherto impossible experiments. Here we review progress in this emerging field.
Collisional resonances are an important tool which has been used to modify interactions in ultracold gases, for realizing novel Hamiltonians in quantum simulations, for creating molecules from atomic gases and for controlling chemical reactions. So far, such resonances have been observed for atom-atom collisions, atom-molecule collisions and collisions between Feshbach molecules which are very weakly bound. Whether such resonances exist for ultracold ground state molecules has been debated due to the possibly high density of states and/or rapid decay of the resonant complex. Here we report a v…
Trapped ultracold Fermi gases provide a system that can be tuned between the BCS and BEC regimes by means of a magnetic-field Feshbach resonance. Condensation of fermionic atom pairs in a $^{40}$K gas was demonstrated experimentally by a sweep technique that pairwise projects fermionic atoms onto molecules. In this paper we examine previous data obtained with this technique that probed the phase boundary in the temperature-magnetic field plane. Comparison of the $^{40}$K data to a theoretically computed phase diagram demonstrates good agreement between the two.
We consider dipolar interactions between heteronuclear molecules in low-dimensional geometries. The setup consists of two one-dimensional tubes. We study the stability of possible few-body complexes in the regime of repulsive intratube interaction, where the binding arises from intertube attraction. The stable dimers, trimers, and tetramers are found and we discuss their properties for both bosonic and fermionic molecules. To observe these complexes we propose an optical non-destructive detection scheme that enables in-situ observation of the creation and dissociation of the few-body complexes…
We have studied the associative ionization of a Rydberg atom and a ground state atom in an ultracold Rydberg gas. The measured scattering cross section is three orders of magnitude larger than the geometrical size of the produced molecule. This giant enhancement of the reaction kinetics is due to an efficient directed mass transport which is mediated by the Rydberg electron. We also find that the total inelastic scattering cross section is given by the geometrical size of the Rydberg electron's wavefunction.
