p-Wave Feshbach molecules

Ultracold field-linked tetratomic molecules

Ultracold polyatomic molecules offer opportunities1 in cold chemistry2,3, precision measurements4 and quantum information processing5,6, because of their rich internal structure. However, their increased complexity compared with diatomic molecules presents a challenge in using conventional cooling techniques. Here we demonstrate an approach to create weakly bound ultracold polyatomic molecules by electroassociation7 (F.D. et al., manuscript in preparation) in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance8-11. Starting from ground-state NaK molecules, we create around 1.1 × 103 weakly bound tetratomic (NaK)2 molecules, with a phase space density of 0.040(3) at a temperature of 134(3) nK, more than 3,000 times colder than previously realized tetratomic molecules12. We observe a maximum tetramer lifetime of 8(2) ms in free space without a notable change in the presence of an optical dipole trap, indicating that these tetramers are collisionally stable. Moreover, we directly image the dissociated tetramers through microwave-field modulation to probe the anisotropy of their wavefunction in momentum space. Our result demonstrates a universal tool for assembling weakly bound ultracold polyatomic molecules from smaller polar molecules, which is a crucial step towards Bose-Einstein condensation of polyatomic molecules and towards a new crossover from a dipolar Bardeen-Cooper-Schrieffer superfluid13-15 to a Bose-Einstein condensation of tetramers. Moreover, the long-lived field-linked state provides an ideal starting point for deterministic optical transfer to deeply bound tetramer states16-18.

Topological Superconductivity in Doped Magnetic Moiré Semiconductors

We show that topological superconductivity may emerge upon doping of transition metal dichalcogenide heterobilayers above an integer-filling magnetic state of the topmost valence moiré band. The effective attraction between charge carriers is generated by an electric p-wave Feshbach resonance arising from interlayer excitonic physics and has a tunable strength, which may be large. Together with the low moiré carrier densities reachable by gating, this robust attraction enables access to the long-sought p-wave BEC-BCS transition. The topological protection arises from an emergent time reversal symmetry occurring when the magnetic order and long wavelength magnetic fluctuations do not couple different valleys. The resulting topological superconductor features helical Majorana edge modes, leading to half-integer quantized spin-thermal Hall conductivity and to charge currents induced by circularly polarized light or other time-reversal symmetry-breaking fields.

Effective Potential and Superfluidity of Microwave-Shielded Polar Molecules

We analytically show that the effective interaction potential between microwave-shielded polar molecules consists of an anisotropic van der Waals-like shielding core and a modified dipolar interaction. This effective potential is validated by comparing its scattering cross sections with those calculated using intermolecular potential involving all interaction channels. It is shown that a scattering resonance can be induced under microwave fields reachable in current experiments. With the effective potential, we further study the Bardeen-Cooper-Schrieffer pairing in the microwave-shielded NaK gas. We show that the superfluid critical temperature is drastically enhanced near the resonance. As the effective potential is suitable for exploring the many-body physics of molecular gases, our results pave the way for studies of the ultracold gases of microwave-shielded molecular gases.

Unitary p-wave interactions between fermions in an optical lattice

Exchange-antisymmetric pair wavefunctions in fermionic systems can give rise to unconventional superconductors and superfluids^1-3. The realization of these states in controllable quantum systems, such as ultracold gases, could enable new types of quantum simulations^4-8, topological quantum gates^9-11 and exotic few-body states^12-15. However, p-wave and other antisymmetric interactions are weak in naturally occurring systems^16,17, and their enhancement via Feshbach resonances in ultracold systems has been limited by three-body loss^18-24. Here we create isolated pairs of spin-polarized fermionic atoms in a multiorbital three-dimensional optical lattice. We spectroscopically measure elastic p-wave interaction energies of strongly interacting pairs of atoms near a magnetic Feshbach resonance. The interaction strengths are widely tunable by the magnetic field and confinement strength, and yet collapse onto a universal curve when rescaled by the harmonic energy and length scales of a single lattice site. The absence of three-body processes enables the observation of elastic unitary p-wave interactions, as well as coherent oscillations between free-atom and interacting-pair states. All observations are compared both to an exact solution using a p-wave pseudopotential and to numerical solutions using an ab initio interaction potential. The understanding and control of on-site p-wave interactions provides a necessary component for the assembly of multiorbital lattice models^25,26 and a starting point for investigations of how to protect such systems from three-body recombination in the presence of tunnelling, for instance using Pauli blocking and lattice engineering^27,28.

Tricritical Physics in Two-Dimensional p-Wave Superfluids

We study effects of quantum fluctuations on two-dimensional p+ip superfluids near resonance. In the standard paradigm, phase transitions between superfluids and zero density vacuum are continuous. When strong quantum fluctuations near resonance are present, the line of continuous phase transitions terminates at two tricritical points near resonance, between which the transitions are expected to be first-order ones. The size of the window where first-order phase transitions occur is shown to be substantial when the coupling is strong. Near first-order transitions, superfluids self-contract due to phase separations between superfluids and vacuum.

Fermi-Liquid Description of a Single-Component Fermi Gas with p-Wave Interactions

We study the Fermi liquid properties of a single component Fermi gas with p-wave interactions. In the weak repulsive limit, we obtain exact perturbative expansions for the ground state energy, the chemical potential, and the effective mass of the Landau quasiparticle up to second order in scattering volume a. We also calculated the corresponding Landau functions and Landau parameters and show that they satisfy the general Fermi liquid identities. Using the Landau transport equation, we show that undamped zero sound only appears in the second order in scattering volume, in contrast to the s-wave case.

Stable p-Wave Resonant Two-Dimensional Fermi-Bose Dimers

We consider two-dimensional weakly bound heterospecies molecules formed in a Fermi-Bose mixture with attractive Fermi-Bose and repulsive Bose-Bose interactions. Bosonic exchanges lead to an intermolecular attraction, which can be controlled and tuned to a p-wave resonance. Such attractive fermionic molecules can be realized in quasi-two-dimensional ultracold isotopic mixtures. We show that they are stable with respect to the recombination to deeply bound molecular states and with respect to the formation of higher-order clusters (trimers, tetramers, etc.).

Scaling Law for Three-Body Collisions of Identical Fermions with p-Wave Interactions

We experimentally confirmed the threshold behavior and scattering length scaling law of the three-body loss coefficients in an ultracold spin-polarized gas of ^{6}Li atoms near a p-wave Feshbach resonance. We measured the three-body loss coefficients as functions of temperature and scattering volume, and we found that the threshold law and the scattering length scaling law hold in limited temperature and magnetic field regions. We also found that the breakdown of the scaling laws is due to the emergence of the effective-range term. This work is an important first step towards a full understanding of the loss of identical fermions with p-wave interactions.

Review of pseudogaps in strongly interacting Fermi gases

A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.

Pairing Dynamics of Polar States in a Quenched p-Wave Superfluid Fermi Gas

We study the pairing dynamics of polar states in a single species p-wave superfluid Fermi gas following a sudden change of the interaction strength. The anisotropy of pair interaction together with the presence of the centrifugal barrier results in profoundly different pairing dynamics compared to the s-wave case. Depending on the direction of quenches, quench to the BCS regime results in large oscillatory depletion of momentum occupation inside the Fermi sea or large oscillatory filling of momentum occupation. A crucial role of the resonant state supported by the centrifugal barrier in the pairing dynamics is elucidated.

Topological Superfluid in a Fermi-Bose Mixture with a High Critical Temperature

We show that a 2D spin-polarized Fermi gas immersed in a 3D Bose-Einstein condensate constitutes a very promising system for realizing a p_{x}+ip_{y} superfluid. The fermions attract each other via an induced interaction mediated by the bosons, and the resulting pairing is analyzed with retardation effects fully taken into account. This is further combined with Berezinskii-Kosterlitz-Thouless (BKT) theory to obtain reliable results for the superfluid critical temperature. We show that both the strength and the range of the induced interaction can be tuned experimentally, which can be used to make the critical temperature approach the maximum value allowed by general BKT theory. Moreover, this is achieved while keeping the Fermi-Bose interaction weak so that three-body losses are small. Our results show that realizing a topological superfluid with atomic Fermi-Bose mixtures is within experimental reach.

Universal Relations for a Fermi Gas Close to a p-Wave Interaction Resonance

We investigate the properties of a spinless Fermi gas close to a p-wave interaction resonance. We show that the effects of interaction near a p-wave resonance are captured by two contacts, which are related to the variation of energy with the p-wave scattering volume v and with the effective range R in two adiabatic theorems. Exact pressure and virial relations are derived. We show how the two contacts determine the leading and subleading asymptotic behavior of the momentum distribution (∼1/k^{2} and ∼1/k^{4}) and how they can be measured experimentally by radio-frequency and photoassociation spectroscopies. Finally, we evaluate the two contacts at high temperature with a virial expansion.

Association of atoms into universal dimers using an oscillating magnetic field

In a system of ultracold atoms near a Feshbach resonance, pairs of atoms can be associated into universal dimers by an oscillating magnetic field with a frequency near that determined by the dimer binding energy. We present a simple expression for the transition rate that takes into account many-body effects through a transition matrix element of the contact. In a thermal gas, the width of the peak in the transition rate as a function of the frequency is determined by the temperature. In a dilute Bose-Einstein condensate of atoms, the width is determined by the inelastic scattering rates of a dimer with zero-energy atoms. Near an atom-dimer resonance, there is a dramatic increase in the width from inelastic atom-dimer scattering and from atom-atom-dimer recombination. The recombination contribution provides a signature for universal tetramers that are Efimov states consisting of two atoms and a dimer.

Dynamical phases in quenched spin-orbit-coupled degenerate Fermi gas

The spin-orbit-coupled degenerate Fermi gas provides a new platform for realizing topological superfluids and related topological excitations. However, previous studies have been mainly focused on the topological properties of the stationary ground state. Here, we investigate the quench dynamics of a spin-orbit-coupled two-dimensional Fermi gas in which the Zeeman field serves as the major quench parameter. Three post-quench dynamical phases are identified according to the asymptotic behaviour of the order parameter. In the undamped phase, a persistent oscillation of the order parameter may support a topological Floquet state with multiple edge states. In the damped phase, the magnitude of the order parameter approaches a constant via a power-law decay, which may support a dynamical topological phase with one edge state at the boundary. In the overdamped phase, the order parameter decays to zero exponentially although the condensate fraction remains finite. These predictions can be observed in the strong-coupling regime.

Quench-induced Floquet topological p-wave superfluids

Ultracold atomic gases in two dimensions tuned close to a p-wave Feshbach resonance were expected to exhibit topological superfluidity, but these were found to be experimentally unstable. We show that one can induce a topological Floquet superfluid if weakly interacting atoms are brought suddenly close ("quenched") to such a resonance, in the time before the instability kicks in. The resulting superfluid possesses Majorana edge modes, yet differs from a conventional Floquet system as it is not driven externally. Instead, the periodic modulation is self-generated by the dynamics.

p-Wave polaron

We consider a single impurity immersed in a Fermi sea close to an interspecies p-wave Feshbach resonance. We calculate its dispersion and spectral response to a radio frequency pulse. In a magnetic field, dipolar interactions split the resonance and two novel features with respect to the s-wave case appear: a third polaron branch in the excitation spectrum, in addition to the usual attractive and repulsive ones; and an anisotropic dispersion of the impurity characterized by different effective masses perpendicular and parallel to the magnetic field. The anisotropy can be tuned as a function of the field strength and the two effective masses may have opposite signs, or become smaller than the bare mass.

Few-body physics with ultracold atomic and molecular systems in traps

Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible-thanks to tremendous progress in cooling, trapping and manipulating ultracold samples-to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two particles, bosons or fermions, are placed in an external confinement. Next, various three-body systems are treated analytically in limiting cases. Our current understanding of larger two-component Fermi systems and Bose systems is reviewed, and connections with the corresponding bulk systems are established. Lastly, future prospects and challenges are discussed. Throughout this review, commonalities with other systems such as nuclei or quantum dots are highlighted.

Volume dependence of bound states with angular momentum

We derive general results for the mass shift of bound states with angular momentum ℓ≥1 in a finite periodic volume. Our results have direct applications to lattice simulations of hadronic molecules as well as atomic nuclei. While the binding of S-wave bound states increases at finite volume, we show that the binding of P-wave bound states decreases. The mass shift for D-wave bound states as well as higher partial waves depends on the representation of the cubic rotation group. Nevertheless, the multiplet-averaged mass shift for any angular momentum ℓ can be expressed in a simple form, and the sign of the shift alternates for even and odd ℓ. We verify our analytical results with explicit numerical calculations. We also show numerically that similar volume corrections appear in three-body bound states.

Phase-sensitive measurements of order parameters for ultracold atoms through two-particle interferometry

Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.

Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.

Simulating the Wess-Zumino supersymmetry model in optical lattices

We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.

Exact solution for 1D spin-polarized fermions with resonant interactions

Using the asymptotic Bethe ansatz, we obtain an exact solution of the many-body problem for 1D spin-polarized fermions with resonant p-wave interactions, taking into account the effects of both scattering volume and effective range. Under typical experimental conditions, accounting for the effective range, the properties of the system are significantly modified due to the existence of "shape" resonances. The excitation spectrum of the considered model has unexpected features, such as the inverted position of the particle- and holelike branches at small momenta, and rotonlike minima. We find that the frequency of the "breathing" mode in the harmonic trap provides an unambiguous signature of the effective range.

p-wave resonant bose gas: a finite-momentum spinor superfluid

We show that a degenerate gas of two-species bosonic atoms interacting through a p-wave Feshbach resonance (as realized in, e.g., a (85)Rb -- (87)Rb mixture) exhibits a finite-momentum atomic-molecular superfluid (AMSF), sandwiched by a molecular p-wave (orbital spinor) superfluid and by an s-wave atomic superfluid at large negative and positive detunings, respectively. The magnetic field can be used to tune the modulation wave vector of the AMSF state, as well as to drive quantum phase transitions in this rich system.

Stabilization of the p-wave superfluid state in an optical lattice

It is hard to stabilize the p-wave superfluid state of cold atomic gas in free space due to inelastic collisional losses. We consider the p-wave Feshbach resonance in an optical lattice, and show that it is possible to have a stable p-wave superfluid state where the multiatom collisional loss is suppressed through the quantum Zeno effect. We derive the effective Hamiltonian for this system, and calculate its phase diagram in a one-dimensional optical lattice. The results show rich phase transitions between the p-wave superfluid state and different types of insulator states induced either by interaction or by dissipation.

px+ipy superfluid from s-wave interactions of fermionic cold atoms

Two-dimensional (p(x)+ip(y)) superfluids or superconductors offer a playground for studying intriguing physics such as quantum teleportation, non-Abelian statistics, and topological quantum computation. Creating such a superfluid in cold fermionic atom optical traps using p-wave Feshbach resonance is turning out to be challenging. Here we propose a method to create a p(x)+ip(y) superfluid directly from an s-wave interaction making use of a topological Berry phase, which can be artificially generated. We discuss ways to detect the spontaneous Hall mass current, which acts as a diagnostic for the chiral p-wave superfluid.

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.

Metastable feshbach molecules in high rotational states

We experimentally demonstrate Cs2 Feshbach molecules well above the dissociation threshold, which are stable against spontaneous decay on the time scale of 1 s. An optically trapped sample of ultracold dimers is prepared in a high rotational state and magnetically tuned into a region with a negative binding energy. The metastable character of these molecules arises from the large centrifugal barrier in combination with negligible coupling to states with low rotational angular momentum. A sharp onset of dissociation with increasing magnetic field is mediated by a crossing with a lower rotational dimer state and facilitates dissociation on demand with a well-defined energy.

Strongly resonant p-wave superfluids

We study theoretically a dilute gas of identical fermions interacting via a p-wave resonance. We show that, depending on the microscopic physics, there are two distinct regimes of p-wave resonant superfluids, which we term "weak" and "strong." Although expected naively to form a paired superfluid, a strongly resonant p-wave superfluid is in fact unstable toward the formation of a gas of fermionic trimers. We examine this instability and estimate the lifetime of the p-wave molecules due to the collisional relaxation into trimers. We discuss consequences for the experimental achievement of p-wave superfluids in both weakly and strongly resonant regimes.

Theory for p-wave Feshbach molecules

We determine the physical properties of p-wave Feshbach molecules in doubly spin-polarized 40K and find excellent agreement with recent experiments. We show that these molecules have a large probability Z to be in the closed channel or bare molecular state responsible for the Feshbach resonance. In the superfluid state this allows for observation of Rabi oscillations between the molecular and atomic components of the Bose-Einstein condensed pairs, which contains a characteristic signature of the quantum phase transition that occurs as a function of applied magnetic field.