Ultracold Fermi Gases Research Articles

Anomalous Weyl superfluid in three-dimensional ultracold fermionic gases

In this paper we use layer construction method to construct an experimentally feasible model to realize one type of anomalous Weyl superfluids (WS) in the context of cold fermionic gases. This exotic phase still characterizes the Weyl points in the bulk but completely different Majorana Fermi arc surface state (MFASS) on the boundaries. In contrast to conventional WS, where MFASS only connects the projection of Weyl points, new MFASS continuously stretches to the border of surface Brillouin zone. We self-consistently determine the phase diagram of model at the mean-field level to claim the achievement of anomalous WS. In addition, inversion symmetry and band inversion in this model are analyzed in detail to provide unique feature of identifying anomalous WS experimentally by momentum-resolved radio-frequency spectroscopy.

Orbital magnetism of ultracold fermionic gases in a lattice: Dynamical mean-field approach

We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including the Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically-ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically-ordered phases, which provides quantitative predictions for on-going and future experiments aiming at approaching and studying long-range ordered states in optical lattices.

Insight into Nearest Neighboring Three- and Four-Electron Processes in a One-Dimensional Correlated Lattice System

Motivated by recent experimental realization of the tunability of many-body interactions in ultracold fermionic gases trapped in optical lattices, we investigate analytically effects of nearest-neighboring diagonal three-body (T) and four-body (F) couplings on the one-dimensional conventional extended Hubbard model with on-site (U) and inter-site (V) interactions. Applying the bosonization and renormalization-group techniques, we present quantum phase diagrams at half filling and in the weak-coupling regime. The result shows that, whether the three-body or four-body effective attraction may give rise to superconducting phases in the region for repulsive U and V. Besides, the four-body coupling can lead to a bond-spin-density-wave phase for F > 0 and a bond-charge-density-wave phase for F < 0.

Anderson localization of Cooper pairs and Majorana fermions in an ultracold atomic Fermi gas with synthetic spin-orbit coupling

We theoretically investigate two-particle and many-particle Anderson localizations of a spin-orbit coupled ultracold atomic Fermi gas trapped in a quasi-periodic potential and subjected to an out-of-plane Zeeman field. We solve exactly the two-particle problem in a finite length system by exact diagonalization and solve approximately the many-particle problem within the mean-field Bogoliubov-de Gennes approach. At a small Zeeman field, the localization properties of the system are similar to that of a Fermi gas with conventional $s$-wave interactions. As the disorder strength increases, the two-particle binding energy increases and the fermionic superfluidity of many particles disappears above a threshold. At a large Zeeman field, where the interatomic interaction behaves effectively like a $p$-wave interaction, the binding energy decreases with increasing disorder strength and the resulting topological superfluidity shows a much more robust stability against disorder than the conventional $s$-wave superfluidity. We also analyze the localization properties of the emergent Majorana fermions in the topological phase. Our results could be experimentally examined in future cold-atom experiments, where the spin-orbit coupling can be induced artificially by using two Raman lasers, and the quasi-periodic potential can be created by using bichromatic optical lattices.

One-dimensional two-orbital SU(N) ultracold fermionic quantum gases at incommensurate filling: A low-energy approach

We investigate the zero-temperature phase diagram of two-orbital SU(N) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the SU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the N=2 case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of 2N fermions.

Coupling Identical one-dimensional Many-Body Localized Systems.

We experimentally study the effects of coupling one-dimensional many-body localized systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artificially prepare an initial charge density wave in an array of 1D tubes with quasirandom on-site disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between many-body localization and Anderson localization. While the noninteracting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system.

Fulde-Ferrell Superfluids without Spin Imbalance in Driven Optical Lattices.

Spin-imbalanced ultracold Fermi gases have been widely studied recently as a platform for exploring the long-sought Fulde-Ferrell-Larkin-Ovchinnikov superfluid phases, but so far conclusive evidence has not been found. Here we propose to realize an Fulde-Ferrell (FF) superfluid without spin imbalance in a three-dimensional fermionic cold atom optical lattice, where s- and p-orbital bands of the lattice are coupled by another weak moving optical lattice. Such coupling leads to a spin-independent asymmetric Fermi surface, which, together with the s-wave scattering interaction between two spins, yields an FF type of superfluid pairing. Unlike traditional schemes, our proposal does not rely on the spin imbalance (or an equivalent Zeeman field) to induce the Fermi surface mismatch and provides a completely new route for realizing FF superfluids.

Rashbon Bound States Associated with a Spherical Spin–Orbit Coupling in an Ultracold Fermi Gas with an s-Wave Interaction

We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin-orbit interaction, $H_{\rm so}=\lambda{\bf p}\cdot{\bf \sigma}$ (where ${\bf \sigma}=(\sigma_x,\sigma_y,\sigma_z)$ are Pauli matrices). Extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR) to include this spin-orbit coupling, we determine the superfluid phase transition temperature $T_{\rm c}$, as functions of the strength of a pairing interaction $U_s$, as well as the spin-orbit coupling strength $\lambda$. Evaluating poles of the NSR particle-particle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the $U_{s}$-$\lambda$ phase diagram. Since the antisymmetric spin-orbit interaction $H_{\rm so}$ breaks the inversion symmetry of the system, rashbon bound states naturally have, not only a spin-singlet and even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus, our results would be also useful for the study of this parity mixing effect in the BCS-BEC crossover regime of a spin-orbit coupled Fermi gas.

Magnetic-Field Dependence of Raman Coupling Strength in Ultracold 40K Atomic Fermi Gas**Supported by the National Basic Research Program of China under Grant No 2011CB921601, the National Natural Science Foundation of China under Grant Nos 11234008, 11361161002 and 11222430, and the Program for Sanjin Scholars of Shanxi Province.

We experimentally demonstrate the relation of Raman coupling strength with the external bias magnetic field in degenerate Fermi gas of 40K atoms. Two Raman lasers couple two Zeeman energy levels, whose energy splitting depends on the external bias magnetic field. The Raman coupling strength is determined by measuring the Rabi oscillation frequency. The characteristics of the Rabi oscillation is to be damped after several periods due to Fermi atoms in different momentum states oscillating with different Rabi frequencies. The experimental results show that the Raman coupling strength will decrease as the external bias magnetic field increases, which is in good agreement with the theoretical prediction.

Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases

Spin-orbit coupling (SOC) is central to many physical phenomena, including fine structures of atomic spectra and quantum topological matters. Whereas SOC is in general fixed in a physical system, atom-laser interaction provides physicists a unique means to create and control synthetic SOC for ultracold atoms \cite{Dalibard}. Though significant experimental progresses have been made, a bottleneck in current studies is the lack of a two-dimensional (2D) synthetic SOC, which is crucial for realizing high-dimensional topological matters. Here, we report the experimental realization of 2D SOC in ultracold $^{40}$K Fermi gases using three lasers, each of which dresses one atomic hyperfine spin state. Through spin injection radio-frequency (rf) spectroscopy, we probe the spin-resolved energy dispersions of dressed atoms, and observe a highly controllable Dirac point created by the 2D SOC. Our work paves the way for exploring high-dimensional topological matters in ultracold atoms using Raman schemes.

Fully controllable Kondo system: Coupling a flux qubit and an ultracold Fermi gas

We show that a composite spin-\textonehalf{} Kondo system can be formed by coupling a superconducting quantum interference device (SQUID) to the internal hyperfine states of a trapped ultracold atomic Fermi gas. Here, the SQUID, or flux qubit, acts as an effective magnetic impurity that induces spin-flip scattering near the Fermi energies of the trapped gas. Although the ultracold gas and SQUID are at vastly different temperatures, the formation of a strongly correlated Kondo state between the two systems is found when the gas is cooled below the Kondo temperature. We find that the Kondo temperature of this hybrid system is within current experimental limits. Furthermore, the momentum distribution of the trapped fermions is calculated, which clearly shows an experimental signature of the Kondo screening length. In addition to probing Kondo physics, the controllability of this system can be used to systematically explore the relaxation and equilibration of a strongly correlated system that has been initially prepared in a selected nonequilibrium state.

Evidence for universal relations describing a gas with p-wave interactions

Thermodynamics provides powerful constraints on physical and chemical systems in equilibrium. However, non-equilibrium dynamics depends explicitly on microscopic properties, requiring an understanding beyond thermodynamics. Remarkably, in dilute gases, a set of universal relations is known to connect thermodynamics directly with microscopic properties. So far, these "contact" relations have been established only for interactions with $s$-wave symmetry, i.e., without relative angular momentum. We report measurements of two new physical quantities, the "$p$-wave contacts", and present evidence that they encode the universal aspects of $p$-wave interactions through recently proposed relations. Our experiments use an ultracold Fermi gas of $^{40}$K, in which $s$-wave interactions are suppressed by polarising the sample, while $p$-wave interactions are enhanced by working near a scattering resonance. Using time-resolved spectroscopy, we study how correlations in the system develop after "quenching" the atoms into an interacting state. Combining quasi-steady-state measurements with new contact relations, we infer an attractive $p$-wave interaction energy as large as half the Fermi energy. Our results reveal new ways to understand and characterise the properties of a resonant $p$-wave quantum gas.

Heat transfer through dipolar coupling: Sympathetic cooling without contact

We consider two parallel layers of dipolar ultracold Fermi gases at different temperatures and calculate the heat transfer between them. The effective interactions describing screening and correlation effects between the dipoles in a single layer are modeled within the Euler-Lagrange Fermi-hypernetted chain approximation. The random-phase approximation is used for the interactions across the layers. We investigate the amount of transferred power between the layers as a function of the temperature difference. Energy transfer arises due to the long-range dipole-dipole interactions. A simple thermal model is established to investigate the feasibility of using the contactless sympathetic cooling of the ultracold polar atoms/molecules. Our calculations indicate that dipolar heat transfer is effective for typical polar molecule experiments and may be utilized as a cooling process.

Topological phases of fermionic ladders with periodic magnetic fields

In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different interesting many-body states were observed. Motivated by these experiments, we extend the uniform synthetic magnetic field to a periodic case and show that a commensurate synthetic magnetic field offers an alternative scheme to realize topological phases in many-body systems of ultra-cold Fermi gases in ladder-like optical lattices. Using the exact diagonalization, we numerically determine the topological band structure, edge states, non-zero Chern numbers, Hofstadter-like-butterfly spectrum, and a complete phase diagram of non-interacting fermionic ladders.

Gaussian fluctuations in the two-dimensional BCS-BEC crossover: finite temperature properties

The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions off- diagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart. Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii- Kosterlitz-Thouless transition has been observed. The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime. The theory is also compared with experimental data. Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.

Specific heat and effects of pairing fluctuations in the BCS-BEC-crossover regime of an ultracold Fermi gas

We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived {\it stable} molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a $^6$Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas, to eventually become stable, as one passes through the BCS-BEC crossover region.

Cooper pairs with zero center-of-mass momentum and their first-order correlation function in a two-dimensional ultracold Fermi gas near a Berezinskii-Kosterlitz-Thouless transition

We investigate the center-of-mass momentum distribution $n_{\boldsymbol Q}$ of Cooper pairs and their first-order correlation function $g_1(r)$ in a strongly interacting two-dimensional Fermi gas. Recently, the BKT (Berezinskii-Kosterlitz-Thouless) transition was reported in a two-dimensional $^6$Li Fermi gas, based on (1) the observations of anomalous enhancement of $n_{{\boldsymbol Q}={\boldsymbol 0}}$ [M. G. Ries, et. al., Phys. Rev. Lett. 114, 230401 (2015)], as well as (2) a power-law behavior of $g_1(r)$ [P. A. Murthy, et. al., Phys. Rev. Lett. 115, 010401 (2015)]. However, including pairing fluctuations within a $T$-matrix approximation (TMA), we show that these results can still be explained as strong-coupling properties of a normal-state two-dimensional Fermi gas. Our results indicate the importance of further experimental observations, to definitely confirm the realization of the BKT transition in this system. Since the BKT transition has been realized in a two-dimensional ultracold Bose gas, our results would be useful for the achievement of this quasi-long range order in an ultracold Fermi gas.

Strong-coupling corrections to spin susceptibility in the BCS-BEC-crossover regime of a superfluid Fermi gas

We theoretically investigate the uniform spin susceptibility $\chi$ in the superfluid phase of an ultracold Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In our previous paper [H. Tajima, {\it et. al.}, Phys. Rev. A {\bf 89}, 033617 (2014)], including pairing fluctuations within an extended $T$-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\chi$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature $T_{\rm c}$. In this paper, we extend this work to the superfluid phase below $T_{\rm c}$, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\chi$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below $T_{\rm c}$ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a $^6$Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.

Velocity-selective electromagnetically-induced-transparency measurements of potassium Rydberg states

We demonstrate a velocity selection scheme that mitigates suppression of electromagnetically induced transparency (EIT) by Doppler shifts for low--high EIT probe--coupling wavelength ordering. An optical pumping beam counter-propagating with the EIT probe beam transfers atoms between hyperfine states in a velocity selective fashion. Measurement of the transmitted probe beam synchronous with chopping of the optical pumping beam enables a Doppler-free EIT signal to be detected. Transition frequencies between 5P$_{1/2}$ and $n$S$_{1/2}$ states for $n=$26, 27, and 28 in $^{39}$K are obtained via EIT spectroscopy in a heated vapor cell with a probe beam stabilized to the 4S$_{1/2}\rightarrow$5P$_{1/2}$ transition. Using previous high-resolution measurements of the 4S$_{1/2}\rightarrow$nS$_{1/2}$ transitions, we make a determination of the absolute frequency of the 4S$_{1/2}\rightarrow$5P$_{1/2}$ transition. Our measurement is shifted by 560 MHz from the currently accepted value with a two-fold improvement in uncertainty. These measurements will enable novel experiments with Rydberg-dressed ultracold Fermi gases composed of $^{40}$K atoms.

Renormalization group analysis of ultracold Fermi gases with two-body attractive interaction

We propose a new functional renormalization group (RG) strategy to investigate the many-body physics of interacting ultracold Fermi gases. By mapping the Ginzburg-Landau (GL) action of Fermi gases onto a complex φ 4-model, we can obtain the closed flow equation in the one-loop approximation. An analysis of the emerging RG flow gives the ground state behavior. The Hamiltonian of a Fermi gas with a two-body attractive interaction is used as a demonstration to clarify our treatment. The fixed point structure reveals not only the condensation phase transition, but also the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. The effect of the imaginary time renormalization is also discussed. It is shown that for the dynamical field configuration our RG procedure can reproduce the well known theoretical results of BCS-BEC crossover, while under a static approximation the phase transition takes place at a higher critical temperature.