We develop a non-Hermitian effective theory for a repulsively interacting Fermi gas in the excited branch. The on-shell $T$-matrix is employed as a complex-valued interaction term, which describes a repulsive interaction between atoms in the excited branch and a two-body inelastic decay to the attractive branch. To see the feature of this model, we have addressed, in the weak coupling regime, the excitation properties of a repulsive Fermi polaron as well as the time-dependent number density. The analytic expressions obtained for these quantities qualitatively show a good agreement with recent experiments. By calculating the dynamical transverse spin susceptibility in the random phase approximation, we show that a ferromagnetic system with nonzero polarization undergoes a dynamical instability and tends towards a heterogeneous phase.
Itinerant ferromagnetism in cold Fermi gases with repulsive interactions is studied applying the Jastrow-Slater approximation generalized to finite polarization and temperature. For two components at zero temperature a second order transition is found at $ak_F\simeq0.90$ compatible with QMC. Thermodynamic functions and observables such as the compressibility and spin susceptibility and the resulting fluctuations in number and spin are calculated. For trapped gases the resulting cloud radii and kinetic energies are calculated and compared to recent experiments. Spin polarized systems are recomm…
Can a gas of spin-up and spin-down fermions become ferromagnetic due to repulsive interactions? This question which has not yet found a definitive theoretical answer was addressed in an experiment with an ultracold two-component Fermi gas. The observation of non-monotonic behavior of lifetime, kinetic energy, and size for increasing repulsive interactions provides strong evidence for a phase transition to a ferromagnetic state. It implies that itinerant ferromagnetism of delocalized fermions is possible without lattice and band structure and validates the most basic model for ferromagnetism in…
Ho claims in his comment that our experiment is direct evidence that itinerant ferromagnetism does not exist in ultracold Fermi gases. This claim is incorrect and based on an invalid estimate of relaxation times and an erroneous interpretation of the detectability of ferromagnetic domains. We point out that the experimental evidence is consistent with the existence of ferromagnetism, but further experiments are needed to distinguish a ferromagnetic ground state from a non-magnetic ground state with ferromagnetic correlations.
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 theoretically investigate the itinerant ferromagnetic transition of a spherically trapped ultracold Fermi gas with spin imbalance under strongly repulsive interatomic interactions. Our study is based on a self-consistent solution of the Hartree-Fock mean-field equations beyond the widely used local density approximation. We demonstrate that, while the local density approximation holds in the paramagnetic phase, after the ferromagnetic transition it leads to a quantitative discrepancy in various thermodynamic quantities even with large atom numbers. We determine the position of the phase tra…
It is argued that ultracold quantum degenerate gas of ytterbium $^{173}$Yb atoms having nuclear spin $I = 5/2$ exhibits an enlarged SU$(6)$ symmetry. Within the Landau Fermi liquid theory, stability criteria against Fermi liquid (Pomeranchuk) instabilities in the spin channel are considered. Focusing on the SU$(n > 2)$ generalizations of ferromagnetism, it is shown within mean-field theory that the transition from the paramagnet to the itinerant ferromagnet is generically first order. On symmetry grounds, general SU$(n)$ itinerant ferromagnetic ground states and their topological excitations a…
We report our realization of a parity-time (PT) symmetric non-Hermitian many-body system using cold atoms with dissipation. After developing a theoretical framework on PT-symmetric many-body systems using ultracold atoms in an optical lattice with controlled dissipation, we describe our experimental setup utilizing one-body atom loss as dissipation with special emphasis on calibration of important system parameters. We discuss loss dynamics observed experimentally.
Non-Hermitian skin effect, which refers to the phenomenon that an extensive number of eigenstates are localized at the boundary, has been widely studied in lattice models and experimentally observed in several classical systems. In this work, we predict that the existence of the non-Hermitian skin effect in the dissipative ultracold fermions with spin-orbit coupling, a continuous model that has been implemented by the Hong-Kong group in a recent experiment. This skin effect is robust against the variation of external parameters and trapping potentials. We further reveal a dynamic sticky effect…
A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures.
Itinerant ferromagnetism, i.e. spontaneous polarization of non-localized particles, is expected to occur for strong repulsive interactions in a spin-1/2 Fermi system. However, this state has proven notoriously hard to find experimentally, both in ultracold gases and in solids. This raises questions about the stability of the itinerant ferromagnetic state itself. Here we develop a new approach to describe both the direct and exchange interactions for a general interaction potential in the path-integral formalism and we apply this method to itinerant ferromagnetism in three-dimensional ultracold…
We investigate the Kondo effect in an open quantum system, motivated by recent experiments with ultracold alkaline-earth(-like) atoms. Because of inelastic collisions and the associated atom losses, this system is described by a complex-valued Kondo interaction and provides a non-Hermitian extension of the Kondo problem. We show that the non-Hermiticity induces anomalous reversion of renormalization-group flows which violate the $g$-theorem due to non-unitarity and produce a quantum phase transition unique to non-Hermiticity. Furthermore, we exactly solve the non-Hermitian Kondo Hamiltonian us…
We study interacting ultracold atoms in a three-dimensional (3D) harmonic trap with spin-selective dissipations, which can be effectively described by non-Hermitian parity-time ($\mathcal{PT}$) symmetric Hamiltonians. By solving the non-Hermitian two-body problem of spin-1/2 (spin-1) bosons in a 3D harmonic trap exactly, we find that the system can exhibit third-order (fifth-order) exceptional point (EP) with ultra-sensitive cube-root (fifth-root) spectral response due to interaction anisotropies in spin channels. We also present the general principle for the creation of high-order EPs and the…
We propose a controllable method for observing interaction induced ferromagnetism in ultracold fermionic atoms loaded in optical superlattices. We first discuss how to probe and control Nagaoka ferromagnetism in an array of isolated plaquettes (four lattice sites arranged in a square). Next, we show that introducing a weak interplaquette coupling destroys the ferromagnetic correlations. To overcome this instability we propose to mediate long-range ferromagnetic correlations among the plaquettes via double-exchange processes. Conditions for experimental realization and techniques to detect such…
We study the influence of particle interaction on a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding non-interacting (linear) system has been shown to have a topological transition described by the average displacement before decay. Here we use this topological quantity to distinguish coherent quantum dynamics from incoherent classical dynamics caused by a breaking of the translational symmetry. We furthermore analyze the behavior by means of a rate equation providing a quantitative description of the incoherent nonlinear dynamics.
Motivated by the first experimental evidence of ferromagnetic behavior in a three-dimensional ultracold atomic gas, we explore the possibility of itinerant ferromagnetism in a trapped two-dimensional atomic gas. Firstly, we develop a formalism that demonstrates how quantum fluctuations drive the ferromagnetic reconstruction first order, and consider the consequences of an imposed population imbalance. Secondly, we adapt this formalism to elucidate the key experimental signatures of ferromagnetism in a realistic trapped geometry.
Non-Hermitian skin effect(NHSE) describes a unique non-Hermitian phenomenon that all eigen-modes are localized near the boundary, and has profound impact on a wide range of bulk properties. In particular, topological systems with NHSE have stimulated extensive research interests recently, given the fresh theoretical and experimental challenges therein. Here we propose a readily implementable scheme for achieving NHSE with band topology in ultracold gases. Specifically, the scheme realizes the one-dimensional optical Raman lattice with two types of spin-orbit coupling (SOC) and an additional la…
Spatiotemporal Non-Hermitian Skin Effect with Floquet-Engineered Ultracold Atoms
Quantum Institute for Light and Atoms, School of Physics, East China Normal University（华东师范大学物理学院光与原子量子研究所）；School of Physics and Astronomy, and Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学物理与天文学院及李政道研究所）；Shanghai Branch, Hefei National Laboratory（合肥国家实验室上海分部）；Shanghai Research Center for Quantum Sciences（上海量子科学研究与创新中心）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.
We investigate two-component ultracold fermions loaded into a decorated square lattice, which are described by the Hubbard model with repulsive interactions and nearest neighbor hoppings. By combining the real-space dynamical mean-field theory with the numerical renormalization group method, we discuss how a ferromagnetically ordered ground state in the weak coupling regime, which originates from the existence of a dispersionless band, is adiabatically connected to a Heisenberg ferrimagnetic state in the strong coupling limit. The effects of level splitting and hopping imbalance are also addre…
The non-Hermitian skin effect (NHSE), the accumulation of eigen wavefunctions at boundaries of open systems, underlies a variety of exotic properties that defy conventional wisdom. While NHSE and its intriguing impact on band topology and dynamics have been observed in classical or photonic systems, their demonstration in a quantum many-body setting remains elusive. Here we report the experimental realization of a dissipative Aharonov-Bohm chain -- a non-Hermitian topological model with NHSE -- in the momentum space of a two-component Bose-Einstein condensate. We identify unique signatures of …
The simplest model for itinerant ferromagnetism, the Stoner model, has so far eluded experimental observation in repulsive ultracold fermions due to rapid three-body recombination at large scattering lengths. Here we show that a ferromagnetic phase can be stabilised by imposing a moderate optical lattice. The reduced kinetic energy drop upon formation of a polarized phase in an optical lattice extends the ferromagnetic phase to smaller scattering lengths where three-body recombination is small enough to permit experimental detection of the phase. We also show, using time dependent density func…
Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the most well-characterized phases of correlated Fermi systems. A recent experiment has reported the first evidence for novel phase behavior on the repulsive side of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting recent theoretical studies to the atomic trap geometry, we show that an adiabatic ferromagnetic transition would take place at a weaker interaction strength than is observed in experiment. This discrepancy motivates a simple non-equilibrium theory that takes account of the dynamics of…
Due to the fundamental position of spin-orbit coupled ultracold atoms in the simulation of topological insulators, the gain/loss effects on these systems should be evaluated when considering the measurement or the coupling to the environment. Here, incorporating the mature gain/loss techniques into the experimentally realized spin-orbit coupled ultracold atoms in two-dimensional optical lattices, we investigate the corresponding non-Hermitian tight-binding model and evaluate the gain/loss effects on various properties of the system, revealing the interplay of the non-Hermiticity and the spin-o…
Recent realizations of quantum gas microscope offer the possibility of continuous monitoring of the dynamics of a quantum many-body system at the single-particle level. By analyzing effective non-Hermitian Hamiltonians of interacting bosons in an optical lattice and continuum, we demonstrate that the backaction of quantum measurement shifts the quantum critical point and gives rise to a unique critical phase beyond the terrain of the standard universality class. We perform mean-field and strong-coupling-expansion analyses and show that non-Hermitian contributions shift the superfluid--to-Mott-…
We analyze when a repulsively interacting two-component Fermi gas becomes thermodynamically unstable against phase separation. We focus on the strongly polarised limit where the free energy of the homogeneous mixture can be calculated accurately in terms of well-defined quasiparticles, the repulsive polarons. Phase diagrams as a function of polarisation, temperature, mass imbalance, and repulsive polaron energy, as well as scattering length and range parameter are provided. We show that the lifetime of the repulsive polaron increases significantly with the interaction range and the mass of the…
We investigate ferromagnetic ordering in an itinerant ultracold atomic Fermi gas with repulsive interactions and population imbalance. In a spatially uniform system, we show that at zero temperature the transition to the itinerant magnetic phase transforms from first to second order with increasing population imbalance. Drawing on these results, we elucidate the phases present in a trapped geometry, finding three characteristic types of behavior with changing population imbalance. Finally, we outline the potential experimental implications of the findings.
Properties of the ground state and the spectrum of elementary excitations are investigated for the low density ultracold spinor 3D Bose gas of particles with arbitrary nonzero spin. Gross-Pitaevskii equations are derived. Within the framework of the considering interaction Hamiltonian it is shown that the ground state spin structure and spin part of the chemical potential is determined by the renormalized interaction, being defined by the contribution of the virtual large momenta. The ferromagnetic structure of the ground state, and the equation of the phase, density, and spin dynamics are obt…
Recent experimental breakthroughs in non-Hermitian ultracold atomic lattices have dangled tantalizing prospects in realizing exotic, hitherto unreported, many-body non-Hermitian quantum phenomena. In this work, we discover and propose an experimental platform for a radically different non-Hermitian phenomenon dubbed polaron squeezing. It is marked by a dipole-like accumulation of fermions arising from an interacting impurity in a background of non-Hermitian reciprocity-breaking hoppings. We computed their spatial density and found that, unlike Hermitian polarons which are symmetrically localiz…
A recent experiment has provided the first evidence for itinerant ferromagnetism in an ultracold atomic gas of fermions with repulsive interactions. However, the gas in this regime is also subject to significant three-body loss. We adopt an extended Hertz-Millis theory to account for the effect of loss on the transition and on the ferromagnetic state. We find that the losses damp quantum fluctuations and thereby significantly increase the critical interaction strength needed to induce ferromagnetism. This effect may resolve a discrepancy between the experiment and previous theoretical predicti…
Using continuous-space quantum Monte Carlo methods we investigate the zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas under the influence of periodic potentials that describe the effect of a simple-cubic optical lattice. Simulations are performed with balanced and with imbalanced components, including the case of a single impurity immersed in a polarized Fermi sea (repulsive polaron). For an intermediate density below half filling, we locate the transitions between the paramagnetic, and the partially and the fully ferromagnetic phases. As the intensity of the opt…
We propose a realizable experiment scheme to construct a one-dimensional synthetic magnetic flux lattice with spin-tensor-momentum coupled spin-1 atoms and explore its exotic topological states. Different from the Altland-Zirnbauer classification, we show that our system hosts a symmetryprotected phase protected by a magnetic group symmetry (M) and characterized by a Z2 topological invariant. In single-particle spectra, we show that the topological nontrivial phase supports two kinds of edge states, which include two (four) zero-energy edge modes in the absence (presence) of two-photon detunin…
We present exact analytic results for the energy of a SU(N) repulsive Fermi gas as a function of the spin-channel occupation at second order in the gas parameter. This is an extension of an old result that now incorporates the degree of polarization of the system. Therefore, the magnetic properties of the gas can be obtained, free from numerical uncertainties. For spin 1/2 we find that second-order corrections change the itinerant ferromagnetic transition from continuous to first-order. Instead, for spin larger than 1/2 the phase transition is always of first-order type. The transition critica…
Recent advances in rapidly quenched ultracold atomic Fermi gases near a Feshbach resonance have brought about a number of interesting problems, in the context of observing the long-sought Stoner ferromagnetic phase transition. The possibility of experimentally obtaining a "quasirepulsive" regime in the upper branch of the energy spectrum due to the rapid quench is currently being debated, and the Stoner transition has mainly been investigated theoretically by using perturbation theory or at high polarization, due to the limited theoretical approaches in the strongly repulsive regime. In this w…
Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions' dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter-Fermi-Hubbard model …
It has long been predicted that a two-component non-localized Fermi gas will exhibit spontaneous polarization for sufficiently strong repulsive interactions, a phenomenon which is called itinerant ferromagnetism. Recent experiments with ultracold atomic gases have reached the interaction strength for which theoretical models have predicted the occurrence of the normal-to-itinerant-ferromagnetic phase transition, but so far this transition has not been observed. The instability of the repulsive branch of the Feshbach resonance prevents the formation of the itinerant ferromagnetic state, but it …
We study a Bose-Einstein condensate of ultracold atoms subject to a non-Hermitian spin-orbit coupling, where the system acquires non-Hermitian skin effect under the interplay of spin-orbit coupling and laser-induced atom loss. The presence of the non-Hermitian skin effect is confirmed through its key signatures in term of the spectral winding under the periodic boundary condition, the accumulation of eigen wavefunctions at boundaries under an open boundary condition, as well as bulk dynamics signaled by a directional flow. We show that the bulk dynamics in particular serves as a convenient sig…
We propose an ultracold-atom setting where a fermionic superfluidity with attractive s-wave interaction is uploaded in a non-Hermitian Lieb optical lattice. The existence of a real-energy flat band solution is revealed. We show that the interplay between the skin effect and flat-band localization leads to exotic localization properties. We develop a multiband mean-field description of this system and use both order parameters and superfluid weight to describe the phase transition. A relation between the superfluid weight and non-Hermitian quantum metric of the quantum states manifold is built.…
We investigate the ground state and quantum dynamics of an interacting bosonic chain with the nonreciprocal hopping. In sharp contrast to its Hermitian counterpart, the ground state can support Mott insulators in systems with noninteger filling due to the competition between nonreciprocal hopping and the on-site interaction. For the quantum dynamics, conservation laws for non-Hermitian systems manifest a stark difference from their Hermitian counterpart. In particular, for any Hermitian operator that commutes with the Hamiltonian operator, its expectation value is guaranteed to be nonconserved…
Spin-orbit coupling is an essential mechanism underlying quantum phenomena such as the spin Hall effect and topological insulators. It has been widely studied in well-isolated Hermitian systems, but much less is known about the role dissipation plays in spin-orbit-coupled systems. Here, we implement dissipative spin-orbit-coupled bands filled with ultracold fermions, and observe parity-time symmetry breaking as a result of the competition between the spin-orbit coupling and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables us to tune the energy gap and close it…
Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of non-diagonalizable exceptional points, lines, and s…
Measurement is one of the most counter-intuitive aspects of quantum physics. Frequent measurements of a quantum system lead to quantum Zeno dynamics where time evolution becomes confined to a subspace defined by the projections. However, weak measurement performed at a finite rate is also capable of locking the system into such a Zeno subspace in an unconventional way: by Raman-like transitions via virtual intermediate states outside this subspace, which are not forbidden. Here, we extend this concept into the realm of non-Hermitian dynamics by showing that the stochastic competition between m…
Quantum degeneracy pressure (QDP) underscores the stability of matter and is arguably the most ubiquitous many-body effect. The associated Fermi surface (FS) has broad implications for physical phenomena, ranging from electromagnetic responses to entanglement entropy (EE) area law violations. Given recent fruitful studies in condensed-matter physics under effectively non-Hermitian descriptions, it becomes urgent to study how QDP and many-body interactions interplay with non-Hermitian effects. Through a prototypical critical 1D fermionic lattice with asymmetric gain/loss, a real space FS is sho…
We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis of a non-Hermitian XXZ spin chain as a prototypical model in one-dimensional open quantum many-body systems. Our analytic calculation is based on effective field theory with bosonization, finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution. Our numerical analysis is based on the density-matrix renormalization group generalized to non-Hermitian systems (NH-DMRG). We uncover that the model in the …
