Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate

Dipolar physics: a review of experiments with magnetic quantum gases

Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.

Topological superfluid defects with discrete point group symmetries

Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose-Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope symmetries in their topological defects. Using carefully tailored spinor rotations and microwave transitions, we engineer singular line defects whose quantization conditions, exchange statistics, and dynamics are fundamentally determined by these underlying symmetries. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries. Such defects, with their non-commutative properties, could provide unconventional realizations of quantum information and interferometry.

Magnetic Dipolar Interaction between Hyperfine Clock States in a Planar Alkali Bose Gas

In atomic systems, clock states feature a zero projection of the total angular momentum and thus a low sensitivity to magnetic fields. This makes them widely used for metrological applications like atomic fountains or gravimeters. Here, we show that a mixture of two such nonmagnetic states still displays magnetic dipole-dipole interactions comparable to the one expected for the other Zeeman states of the same atomic species. Using high-resolution spectroscopy of a planar gas of ^{87}Rb atoms with a controlled in plane shape, we explore the effective isotropic and extensive character of these interactions and demonstrate their tunability. Our measurements set strong constraints on the relative values of the s-wave scattering lengths a_{ij} involving the two clock states.

Collisions of Three-Component Vector Solitons in Bose-Einstein Condensates

Ultracold gases provide an unprecedented level of control for the investigation of soliton dynamics and collisions. We present a scheme for deterministically preparing pairs of three-component solitons in a Bose-Einstein condensate. Our method is based on local spin rotations which simultaneously imprint suitable phase and density distributions. This enables us to observe striking collisional properties of the vector degree of freedom which naturally arises for the coherent nature of the emerging multicomponent solitons. We find that the solitonic properties in the quasi-one-dimensional system are quantitatively described by the integrable repulsive three-component Manakov model.

Magnetic Solitons in a Spin-1 Bose-Einstein Condensate

Vector solitons are a type of solitary or nonspreading wave packet occurring in a nonlinear medium composed of multiple components. As such, a variety of synthetic systems can be constructed to explore their properties, from nonlinear optics to ultracold atoms, and even in metamaterials. Bose-Einstein condensates have a rich panoply of internal hyperfine levels, or spin components, which make them a unique platform for exploring these solitary waves. However, existing experimental work has focused largely on binary systems confined to the Manakov limit of the nonlinear equations governing the soliton behavior, where quantum magnetism plays no role. Here we observe, using a "magnetic shadowing" technique, a new type of soliton in a spinor Bose-Einstein condensate, one that exists only when the underlying interactions are antiferromagnetic and which is deeply embedded within a full spin-1 quantum system. Our approach opens up a vista for future studies of "solitonic matter" whereby multiple solitons interact with one another at deterministic locations.

Observation of Spin-Spin Fermion-Mediated Interactions between Ultracold Bosons

Interactions in an ultracold boson-fermion mixture are often manifested by elastic collisions. In a mixture of a condensed Bose gas (BEC) and spin polarized degenerate Fermi gas (DFG), fermions can mediate spin-spin interactions between bosons, leading to an effective long-range magnetic interaction analogous to Ruderman-Kittel-Kasuya-Yosida [Phys. Rev. 96, 99 (1954); Prog. Theor. Phys. 16, 45 (1956); Phys. Rev. 106, 893 (1957)] interaction in solids. We used Ramsey spectroscopy of the hyperfine clock transition in a ^{87}Rb BEC to measure the interaction mediated by a ^{40}K DFG. By controlling the boson density we isolated the effect of mediated interactions from mean-field frequency shifts due to direct collision with fermions. We measured an increase of boson spin-spin interaction by a factor of η=1.45±0.05^{stat}±0.13^{syst} in the presence of the DFG, providing clear evidence of spin-spin fermion mediated interaction. Decoherence in our system was dominated by inhomogeneous boson density shift, which increased significantly in the presence of the DFG, again indicating mediated interactions. We also measured a frequency shift due to boson-fermion interactions in accordance with a scattering length difference of a_{bf_{2}}-a_{bf_{1}}=-5.36±0.44^{stat}±1.43^{syst}a_{0} between the clock-transition states, a first measurement beyond the low-energy elastic approximation [R. Côté, A. Dalgarno, H. Wang, and W. C. Stwalley, Phys. Rev. A 57, R4118 (1998); A. Dalgarno and M. Rudge, Proc. R. Soc. A 286, 519 (1965)] in this mixture. This interaction can be tuned with a future use of a boson-fermion Feshbach resonance. Fermion-mediated interactions can potentially give rise to interesting new magnetic phases and extend the Bose-Hubbard model when the atoms are placed in an optical lattice.

Simultaneous Readout of Noncommuting Collective Spin Observables beyond the Standard Quantum Limit

We augment the information extractable from a single absorption image of a spinor Bose-Einstein condensate by coupling to initially empty auxiliary hyperfine states. Performing unitary transformations in both the original and auxiliary hyperfine manifold enables the simultaneous measurement of multiple spin-1 observables. We apply this scheme to an elongated atomic cloud of ^{87}Rb to simultaneously read out three orthogonal spin directions and with that directly access the spatial spin structure. The readout even allows the extraction of quantum correlations which we demonstrate by detecting spin-nematic squeezing without state tomography.

Non-Hermitian Magnon-Photon Interference in an Atomic Ensemble

The interference of photons in a lossy beam splitter (BS) exhibits anticoalescence, which is surprising for bosons. Such a non-Hermitian system involving open quantum dynamics is of particular interest for quantum information processing and metrology. The Hermiticity of photonic devices is generally fixed according to the material, but is controllable at the interface of photons and atomic systems. Here, we demonstrate a tunable non-Hermitian BS for the interference between traveling photonic and localized magnonic modes. The crossover from a Hermitian to a non-Hermitian magnon-photon BS is achieved by controlling the coherent and incoherent interaction mediated by the excited levels of atoms, which is reconfigurable via the detuning of a control laser. A correlated interference pattern between the photons and magnons is demonstrated by such a non-Hermitian BS. Our system has the potential to operate with photons and magnons at the single-quanta level, and it provides a versatile quantum interface for studying the non-Hermitian quantum physics and parity-time symmetry.

Beliaev Damping of a Spin-Orbit-Coupled Bose-Einstein Condensate

Beliaev damping provides a fundamental mechanism for dissipation of quasiparticles. Previous research has shown that the two-component internal degrees of freedom has no nontrivial effect on Beliaev damping. Here we provide the first example where the spinor nature of Bose gases can manifest itself in the Beliaev damping by way of spin-obit coupling. We identify novel features of the Beliaev decay rate due to spin-orbit coupling; in particular, it shows an explicit dependence on the spin-density interaction and diverges at the interaction-modified phase boundary between the zero-momentum and plane wave phases. This represents a manifestation of the effect of spin-orbit coupling in the beyond-mean-field regime, which by breaking Galilean invariance couples excitations in the density and spin channels. We further show that the measurement of the Beliaev damping rate is experimentally feasible through the measurement of spin polarizability susceptibility, which has been already achieved in spin-orbit-coupled Bose gases.

Quantum Field Theory of Nematic Transitions in Spin-Orbit-Coupled Spin-1 Polar Bosons

We theoretically study an ultracold gas of spin-1 polar bosons in a one-dimensional continuum, which are subject to linear and quadratic Zeeman fields and a Raman induced spin orbit coupling. Concentrating on the regime in which the background fields can be treated perturbatively, we analytically solve the model in its low-energy sector; i.e., we characterize the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field ε, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-disordered superfluid phase at strong coupling. We employ a combination of renormalization group calculations and duality transformations to access the nature of the phase transitions. At ε=0, a line of spin-charge separated pairs of Luttinger liquids divides the two nematic phases, and the transition to the spin-disordered state at strong coupling is of the Berezinskii-Kosterlitz-Thouless type. In contrast, at ε≠0, the quantum critical theory separating nematic and strong coupling spin-disordered phases contains a Luttinger liquid in the charge sector that is coupled to a Majorana fermion in the spin sector (i.e., the critical theory at finite ε maps to a quantum critical Ising model that is coupled to the charge Luttinger liquid). Because of an emergent Lorentz symmetry, both have the same logarithmically diverging velocity. We discuss the experimental signatures of our findings that are relevant to ongoing experiments in ultracold atomic gases of ^{23}Na.

Collective Spin Modes of a Trapped Quantum Ferrofluid

We report on the observation of a collective spin mode in a spinor Bose-Einstein condensate. Initially, all spins point perpendicular to the external magnetic field. The lowest energy mode consists of a sinusoidal oscillation of the local spin around its original axis, with an oscillation amplitude that linearly depends on the spatial coordinates. The frequency of the oscillation is set by the zero-point kinetic energy of the BEC. The observations are in excellent agreement with hydrodynamic equations. The observed spin mode has a universal character, independent of the atomic spin and spin-dependent contact interactions.

Imaging Optical Frequencies with 100 μHz Precision and 1.1 μm Resolution

We implement imaging spectroscopy of the optical clock transition of lattice-trapped degenerate fermionic Sr in the Mott-insulating regime, combining micron spatial resolution with submillihertz spectral precision. We use these tools to demonstrate atomic coherence for up to 15 s on the clock transition and reach a record frequency precision of 2.5×10^{-19}. We perform the most rapid evaluation of trapping light shifts and record a 150 mHz linewidth, the narrowest Rabi line shape observed on a coherent optical transition. The important emerging capability of combining high-resolution imaging and spectroscopy will improve the clock precision, and provide a path towards measuring many-body interactions and testing fundamental physics.

Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition

Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.

Observation of Attractive and Repulsive Polarons in a Bose-Einstein Condensate

The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic ^{39}K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity. The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states. Crucially, no significant effects of three-body decay are observed. Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.

Bose Polarons in the Strongly Interacting Regime

When an impurity is immersed in a Bose-Einstein condensate, impurity-boson interactions are expected to dress the impurity into a quasiparticle, the Bose polaron. We superimpose an ultracold atomic gas of ^{87}Rb with a much lower density gas of fermionic ^{40}K impurities. Through the use of a Feshbach resonance and radio-frequency spectroscopy, we characterize the energy, spectral width, and lifetime of the resultant polaron on both the attractive and the repulsive branches in the strongly interacting regime. The width of the polaron in the attractive branch is narrow compared to its binding energy, even as the two-body scattering length diverges.

Condensing Magnons in a Degenerate Ferromagnetic Spinor Bose Gas

We observe the quasicondensation of magnon excitations within an F=1 ^{87}Rb spinor Bose-Einstein condensed gas. Magnons are pumped into a ferromagnetically ordered gas, allowed to equilibrate to a nondegenerate distribution, and then cooled evaporatively at near-constant net longitudinal magnetization, whereupon they condense. The critical magnon number, spatial distribution, and momentum distribution indicate that magnons condense in a potential that is uniform within the volume of the ferromagnetic condensate. The macroscopic transverse magnetization produced by the degenerate magnon gas remains inhomogeneous within the ∼10  s equilibration time accessed in our experiment, and includes signatures of Mermin-Ho spin textures that appear as phase singularities in the magnon quasicondensate wave function.

Quantum mass acquisition in spinor Bose-Einstein condensates

Quantum mass acquisition, in which a massless (quasi)particle becomes massive due to quantum corrections, is predicted to occur in several subfields of physics. However, its experimental observation remains elusive since the emergent energy gap is too small. We show that a spinor Bose-Einstein condensate is an excellent candidate for the observation of such a peculiar phenomenon as the energy gap turns out to be 2 orders of magnitude larger than the zero-point energy. This extraordinarily large energy gap is a consequence of the dynamical instability. The propagation velocity of the resultant massive excitation mode is found to be decreased by the quantum corrections as opposed to phonons.

Quantum phase transitions in networks of Lipkin-Meshkov-Glick models

We study the quantum critical behavior of networks consisting of Lipkin-Meshkov-Glick models with an anisotropic ferromagnetic coupling. We focus on the low-energy properties of the system within a mean-field approach and the quantum corrections around the mean-field solution. Our results show that the weak-coupling regime corresponds to the paramagnetic phase when the local field dominates the dynamics, but the local anisotropy leads to the existence of an exponentially degenerate ground state. In the strong-coupling regime, the ground state is twofold degenerate and possesses long-range magnetic ordering. Analytical results for a network with the ring topology are obtained.