- PRLLocalization on a Synthetic Hall CylinderRen Zhang, Yangqian Yan, and Qi ZhouPhys. Rev. Lett. 126, 193001 (2021)
By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon into a synthetic Hall cylinder could naturally lead to localization. Unlike a Hall ribbon, a Hall cylinder hosts an intrinsic lattice, which arises due to the periodic boundary condition in the azimuthal direction, in addition to the external periodic potential imposed by extra lasers. When these two lattices are incommensurate, localization may occur on a synthetic Hall cylinder. Near the localization-delocalization transitions, the dependence of physical observables on the axial magnetic flux allows us to tackle a fundamental question of determining the accuracy of rational approximation of irrational numbers. In the irrational limit, physical observables are no longer affected by fluctuations of the axial flux.
- arXivEfimov-like states and quantum funneling effects on synthetic hyperbolic surfacesRen Zhang, Chenwei Lv, Yangqian Yan, and Qi ZhouarXiv:2010.05135
Engineering lattice models with tailored inter-site tunnelings and onsite energies could synthesize essentially arbitrary Riemannian surfaces with highly tunable local curvatures. Here, we point out that discrete synthetic Poincaré half-planes and Poincaré disks, which are created by lattices in flat planes, support infinitely degenerate eigenstates for any nonzero eigenenergies. Such Efimov-like states exhibit a discrete scaling symmetry and imply an unprecedented apparatus for studying quantum anomaly using hyperbolic surfaces. Furthermore, all eigenstates are exponentially localized in the hyperbolic coordinates, signifying the first example of quantum funneling effects in Hermitian systems. As such, any initial wave packet travels towards the edge of the Poincaré half-plane or its equivalent on the Poincaré disk, delivering an efficient scheme to harvest light and atoms in two dimensions. Our findings unfold the intriguing properties of hyperbolic spaces and suggest that Efimov states may be regarded as a projection from a curved space with an extra dimension.
- PRXEvidence for bosonization in a three-dimensional gas of SU (N) fermionsPhys. Rev. X 10, 041053 (2020)
Blurring the boundary between bosons and fermions lies at the heart of a wide range of intriguing quantum phenomena in multiple disciplines, ranging from condensed matter physics and atomic, molecular, and optical physics to high-energy physics. One such example is a multicomponent Fermi gas with SU(N) symmetry that is expected to behave like spinless bosons in the large-N limit, where the large number of internal states weakens constraints from the Pauli exclusion principle. However, bosonization in SU(N) fermions has never been established in high dimensions where exact solutions are absent. Here, we report direct evidence for bosonization in a SU(N) fermionic ytterbium gas with tunable N in three dimensions (3D). We measure contacts, the central quantity controlling dilute quantum gases, from the momentum distribution and find that the contact per spin approaches a constant with a 1/N scaling in the low-fugacity regime consistent with our theoretical prediction. This scaling signifies the vanishing role of the fermionic statistics in thermodynamics and allows us to verify bosonization through measuring a single physical quantity. Our work delivers a highly controllable quantum simulator to exchange the bosonic and fermionic statistics through tuning the internal degrees of freedom in any generic dimensions. It also suggests a new route toward exploring multicomponent quantum systems and their underlying symmetries with contacts.
- PRREternal discrete time crystal beating the Heisenberg limitChangyuan Lyu, Sayan Choudhury, Chenwei Lv, Yangqian Yan, and Qi ZhouPhys. Rev. Research 2, 033070 (2020)
A discrete time crystal (DTC) repeats itself with a rigid rhythm, mimicking a ticking clock set by the interplay between its internal structures and an external force. Discrete time crystals promise profound applications in precision timekeeping and other quantum techniques. However, it has been facing a grand challenge of thermalization. The periodic driving supplying the power may ultimately bring DTCs to thermal equilibrium and destroy their coherence. Here we show that an all-to-all interaction delivers a DTC that evades thermalization and maintains quantum coherence and quantum synchronization regardless of spatial inhomogeneities in the driving field and the environment. Moreover, the sensitivity of this DTC scales with the total particle number to the power of 3/2, realizing a quantum device of measuring the driving frequency or the interaction strength beyond the Heisenberg limit. Our work paves the way for designing nonequilibrium phases with long coherence time to advance quantum metrology.
- PRLEmergent Periodic and Quasiperiodic Lattices on Surfaces of Synthetic Hall Tori and Synthetic Hall CylindersYangqian Yan, Shao-Liang Zhang, Sayan Choudhury, and Qi ZhouPhys. Rev. Lett. 123, 260405 (2019)
Synthetic spaces allow physicists to bypass constraints imposed by certain physical laws in experiments. Here, we show that a synthetic torus, which consists of a ring trap in the real space and internal states of ultracold atoms cyclically coupled by Laguerre-Gaussian Raman beams, could be threaded by a net effective magnetic flux through its surface—an impossible mission in the real space. Such a synthetic Hall torus gives rise to a periodic lattice in real dimensions, in which the periodicity of the density modulation of atoms fractionalizes that of the Hamiltonian. Correspondingly, the energy spectrum is featured by multiple bands grouping into clusters with nonsymmorphic-symmetry-protected band crossings in each cluster, leading to swaps of wave packets in Bloch oscillations. Our scheme allows physicists to glue two synthetic Hall tori such that localization may emerge in a quasicrystalline lattice. If the Laguerre-Gaussian Raman beams and ring traps were replaced by linear Raman beams and ordinary traps, a synthetic Hall cylinder could be realized and deliver many of the aforementioned phenomena.
- arXivA Bose-Einstein Condensate on a Synthetic Hall CylinderarXiv:1809.02122
Interplay between matter and fields in physical spaces with nontrivial geometries gives rise to many exotic quantum phenomena. However, their realizations are often impeded by experimental constraints. Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux, topologically equivalent to a two-dimensional (2D) Hall ribbon with two edges connected. This cylindrical surface comprises a real spatial dimension and a curved synthetic dimension formed by cyclically-coupled spin states. The BEC on such a Hall cylinder has counterintuitive properties unattainable by its counterparts in 2D planes. We observe Bloch oscillations of the BEC with doubled periodicity of the band structure, analogous to traveling on a Mobiüs strip, reflecting the BEC’s emergent crystalline order with nonsymmorphic symmetry-protected band crossings. We further demonstrate such topological operations as gapping the band crossings and unzipping the cylinder. Our work opens the door to engineering synthetic curved spaces and observing intriguing quantum phenomena inherent to the topology of spaces.
- PRLYang Monopoles and Emergent Three-Dimensional Topological Defects in Interacting BosonsYangqian Yan, and Qi ZhouPhys. Rev. Lett. 120, 235302 (2018)
The Yang monopole as a zero-dimensional topological defect has been well established in multiple fields in physics. However, it remains an intriguing question to understand the interaction effects on Yang monopoles. Here, we show that the collective motion of many interacting bosons gives rise to exotic topological defects that are distinct from Yang monopoles seen by a single particle. Whereas interactions may distribute Yang monopoles in the parameter space or glue them to a single giant one of multiple charges, three-dimensional topological defects also arise from continuous manifolds of degenerate many-body eigenstates. Their projections in lower dimensions lead to knotted nodal lines and nodal rings. Our results suggest that ultracold bosonic atoms can be used to create emergent topological defects and directly measure topological invariants that are not easy to access in solids.
- PRLObservation of Quantum Interference and Coherent Control in a Photochemical ReactionDavid B. Blasing, Jesús Pérez-Ríos, Yangqian Yan, Sourav Dutta, Chuan-Hsun Li, Qi Zhou, and Yong P. ChenPhys. Rev. Lett. 121, 073202 (2018)
Coherent control of reactants remains a long-standing challenge in quantum chemistry. In particular, we have studied laser-induced molecular formation (photoassociation) in a Raman-dressed spin-orbit-coupled 87Rb Bose-Einstein condensate, whose spin quantum state is a superposition of multiple bare spin components. In contrast to the notably different photoassociation-induced fractional atom losses observed for the bare spin components of a statistical mixture, a superposition state with a comparable spin composition displays the same fractional loss on every spin component. We interpret this as the superposition state itself undergoing photoassociation. For superposition states induced by a large Raman coupling and zero Raman detuning, we observe a nearly complete suppression of the photoassociation rate. This suppression is consistent with a model based upon quantum destructive interference between two photoassociation pathways for colliding atoms with different spin combinations. This model also explains the measured dependence of the photoassociation rate on the Raman detuning at a moderate Raman coupling. Our work thus suggests that preparing atoms in quantum superpositions may represent a powerful new technique to coherently control photochemical reactions.
- JPBPath integral Monte Carlo ground state approach: formalism, implementation, and applicationsYangqian Yan, and D BlumeJ. Phys. B: At. Mol. Opt. Phys. 50, 223001 (2017)
Monte Carlo techniques have played an important role in understanding strongly correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at ﬁnite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Speciﬁcally, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few- or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented.
- THESISPath integral Monte Carlo studies of ultracold few-atom systemsYangqian YanPh.D. Thesis, Washington State University (2016)
Motivated by the fact that ultracold atomic systems can nowadays be realized experimentally with varying number of particles, this thesis explores the transition from few- to many-body physics in ultracold matter via the path-integral Monte Carlo (PIMC) technique. The PIMC approach, which accounts for the particle statistics and yields thermodynamic observables, can be applied to both small and large systems. We determine the energy, Tan’s contact, various structural properties, the super- fluid fraction and density, and the condensate fraction of small harmonically trapped bosonic and fermionic systems as functions of the temperature and s-wave scattering length. We find that the superfluid fraction of fermions is negative for certain parameter combinations and develop a microscopic understanding of this, at first sight, surprising behavior. We further illustrate that the superfluid fraction and condensate fraction are distinct quantities by performing finite temperature two-body calculations. A simple model that can be used to extract the ground state energy of N-boson droplets from finite temperature calculations is proposed. This approach, combined with a novel two-body zero-range propagator, is used to explore the generalized Efimov scenario at unitarity. For three bosons, Efimov predicted the existence of an infinite series of geometrically spaced bound states. Whether the N-boson energy is fully determined by three-body physics or dependent on higher-body properties has long been debated in the literature. We find that the N-body ground state energies display a notable model-dependence, suggesting that corrections to Efimov universality become increasingly more important with increasing N. For van der Waals systems, a weaker universality is found. The equation of state (EOS) of spin-balanced equal-mass two-component Fermi gases at unitarity has been determined in cold atom experiments. At high temperature or low density, the virial expansion provides a good description of the EOS. While the second- and third-order virial coefficients have been calculated theoretically and verified experimentally, theory and experiment do not yet agree on the fourth-order virial coefficient. Our ab initio determination of the fourth-order virial coefficient agrees with experiments, thereby settling an ongoing debate in the literature.
- PRLPath-Integral Monte Carlo Determination of the Fourth-Order Virial Coefficient for a Unitary Two-Component Fermi Gas with Zero-Range InteractionsPhys. Rev. Lett. 116, 230401 (2016)
The unitary equal-mass Fermi gas with zero-range interactions constitutes a paradigmatic model system that is relevant to atomic, condensed matter, nuclear, particle, and astrophysics. This work determines the fourth-order virial coefficient b4 of such a strongly interacting Fermi gas using a customized ab initio path-integral Monte Carlo (PIMC) algorithm. In contrast to earlier theoretical results, which disagreed on the sign and magnitude of b4, our b4 agrees within error bars with the experimentally determined value, thereby resolving an ongoing literature debate. Utilizing a trap regulator, our PIMC approach determines the fourth-order virial coefficient by directly sampling the partition function. An on-the-fly antisymmetrization avoids the Thomas collapse and, combined with the use of the exact two-body zero-range propagator, establishes an efficient general means to treat small Fermi systems with zero-range interactions.
- PRADynamics of small trapped one-dimensional Fermi gas under oscillating magnetic fieldsX. Y. Yin, Yangqian Yan, and D. Hudson SmithPhys. Rev. A 94, 043639 (2016)
Deterministic preparation of an ultracold harmonically trapped one-dimensional Fermi gas consisting of a few fermions has been realized by the Heidelberg group. Using Floquet formalism, we study the time dynamics of two- and three-fermion systems in a harmonic trap under an oscillating magnetic field. The oscillating magnetic field produces a time-dependent interaction strength through a Feshbach resonance. We explore the dependence of these dynamics on the frequency of the oscillating magnetic field for noninteracting, weakly interacting, and strongly interacting systems. We identify the regimes where the system can be described by an effective two-state model and an effective three-state model. We find an unbounded coupling to all excited states at the infinitely strong interaction limit and several simple relations that characterize the dynamics. Based on our findings, we propose a technique for driving transition from the ground state to the excited states using an oscillating magnetic field.
- PRAEnergy and structural properties of N -boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulatorPhys. Rev. A 92, 033626 (2015)
The low-energy spectrum of N-boson clusters with pairwise zero-range interactions is believed to be governed by a three-body parameter. We study the ground state of N-boson clusters with infinite two-body s-wave scattering length by performing ab initio Monte Carlo simulations. To prevent Thomas collapse, different finite-range three-body regulators are used. The energy and structural properties for the three-body Hamiltonian with two-body zero-range interactions and three-body regulator are in much better agreement with the “ideal zero-range Efimov theory” results than those for Hamiltonian with two-body finite-range interactions. For larger clusters we find that the ground-state energy and structural properties of the Hamiltonian with two-body zero-range interactions and finite-range three-body regulators are not universally determined by the three-body parameter, i.e., dependencies on the specific form of the three-body regulator are observed. For comparison, we consider Hamiltonian with two-body van der Waals interactions and no three-body regulator. For the interactions considered, the ground-state energy of the N-body clusters is—if scaled by the three-body ground-state energy—fairly universal, i.e., the dependence on the short-range details of the two-body van der Waals potentials is small. Our results are compared with those in the literature.
- PRAIncorporating exact two-body propagators for zero-range interactions into N -body Monte Carlo simulationsPhys. Rev. A 91, 043607 (2015)
Ultracold atomic gases are, to a very good approximation, described by pairwise zero-range interactions. This paper demonstrates that N-body systems with two-body zero-range interactions can be treated reliably and efficiently by the finite-temperature and ground-state path-integral Monte Carlo approaches, using the exact two-body propagator for zero-range interactions in the pair product approximation. Harmonically trapped one- and three-dimensional systems are considered. A propagator for the harmonically trapped two-body system with infinitely strong zero-range interaction, which may also have applications in real time evolution schemes, is presented.
- PRAOne-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branchSeyed Ebrahim Gharashi, X. Y. Yin, Yangqian Yan, and D. BlumePhys. Rev. A 91, 013620 (2015)
The transition from “few to many” has recently been probed experimentally in an ultracold harmonically confined one-dimensional lithium gas, in which a single impurity atom interacts with a background gas consisting of one, two, or more identical fermions [A. N. Wenz et al., Science 342, 457 (2013)]. For repulsive interactions between the background or majority atoms and the impurity, the interaction energy for relatively moderate system sizes was analyzed and found to converge toward the corresponding expression for an infinitely large Fermi gas. Motivated by these experimental results, we apply perturbative techniques to determine the interaction energy for weak and strong coupling strengths and derive approximate descriptions for the interaction energy for repulsive interactions with varying strength between the impurity and the majority atoms and any number of majority atoms.
- PRLAbnormal Superfluid Fraction of Harmonically Trapped Few-Fermion SystemsPhys. Rev. Lett. 112, 235301 (2014)
Superfluidity is a fascinating phenomenon that, at the macroscopic scale, leads to dissipationless flow and the emergence of vortices. While these macroscopic manifestations of superfluidity are well described by theories that have their origin in Landau’s two-fluid model, our microscopic understanding of superfluidity is far from complete. Using analytical and numerical ab initio approaches, this Letter determines the superfluid fraction and local superfluid density of small harmonically trapped two-component Fermi gases as a function of the interaction strength and temperature. At low temperature, we find that the superfluid fraction is, in certain regions of the parameter space, negative. This counterintuitive finding is traced back to the symmetry of the system’s ground state wave function, which gives rise to a diverging quantum moment of inertia I_q. Analogous abnormal behavior of I_q has been observed in even-odd nuclei at low temperature. Our predictions can be tested in modern cold atom experiments.
- PRLGeneralized Efimov Scenario for Heavy-Light MixturesD. Blume, and Yangqian YanPhys. Rev. Lett. 113, 213201 (2014)
Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of N-1 non-interacting identical heavy bosons, which interact with a light impurity through a large s-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies E_4^(n,1) and E_4^(n,2), which are universally linked to the energy E_3^(n) of the nth Efimov trimer. For infinitely large ^133Cs-^6Li and vanishing ^133Cs-^133Cs scattering lengths, we find (E_4^(1,1)/E_3^(1))^1/2 ≈1.51 and (E_4^(1,2)/E_3^(1))^1/2 ≈1.01. The ^133Cs-^6Li scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for N>4 are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.
- PRATemperature dependence of small harmonically trapped atom systems with Bose, Fermi, and Boltzmann statisticsPhys. Rev. A 90, 013620 (2014)
While the zero-temperature properties of harmonically trapped cold few-atom systems have been discussed fairly extensively over the past decade, much less is known about the finite-temperature properties. Working in the canonical ensemble, we characterize small harmonically trapped atomic systems as a function of the temperature using analytical and numerical techniques. We present results for the energetics, structural properties, condensate fraction, superfluid fraction, and superfluid density. Our calculations for the two-body system underline that the condensate and superfluid fractions are distinctly different quantities. Our work demonstrates that the path-integral Monte Carlo method yields reliable results for bosonic and fermionic systems over a wide temperature range, including the regime where the de Broglie wavelength is large, i.e., where the statistics plays an important role. The regime where the Fermi sign problem leads to reasonably large signal-to-noise ratios is mapped out for selected parameter combinations. Our calculations for bosons focus on the unitary regime, where the physics is expected to be governed by the three-body parameter. If the three-body parameter is large compared to the inverse of the harmonic oscillator length, we find that the bosons form a droplet at low temperature and behave approximately like a noninteracting Bose and eventually Boltzmann gas at high temperature. The change of the behavior occurs over a fairly narrow temperature range. A simple model that reproduces the key aspects of the phase-transition-like feature, which can potentially be observed in cold atom Bose gas experiments, is presented.
- PRAHarmonically trapped Fermi gas: Temperature dependence of the Tan contactPhys. Rev. A 88, 023616 (2013)
Ultracold atomic gases with short-range interactions are characterized by a number of universal species-independent relations. Many of these relations involve the two-body Tan contact. Employing the canonical ensemble, we determine the Tan contact for small harmonically trapped two-component Fermi gases at unitarity over a wide range of temperatures, including the zero and high-temperature regimes. A cluster expansion that describes the properties of the N-particle system in terms of those of smaller subsystems is introduced and shown to provide an accurate description of the contact in the high-temperature regime. Finite-range corrections are quantified and the role of the Fermi statistics is elucidated by comparing results for Fermi, Bose, and Boltzmann statistics.