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arXiv2024

Bounding the Sample Fluctuation for Pure States Certification with Local Random Measurement

Remarkable breakthroughs in quantum science and technology are demanding for more efficient methods in analyzing quantum many-body states. A significant challenge in this field is to verify whether a quantum state prepared by quantum devices in the lab accurately matches the desired target pure state. Recent advancements in randomized measurement techniques have provided fresh insights in this area. Specifically, protocols such as classical shadow tomography and shadow overlap have been proposed. Building on these developments, we investigate the fundamental properties of schemes that certify pure quantum states through random local Haar measurements. We derive bounds for sample fluctuations that are applicable regardless of the specific estimator construction. These bounds depend on the operator size distribution of either the observable used to estimate fidelity or the valid variation of the reduced density matrix for arbitrary observables. Our results unveil the intrinsic interplay between operator complexity and the efficiency of quantum algorithms, serving as an obstacle to local certification of pure states with long-range entanglement.

quant-ph↗

arXiv2026

Coherent Control of Domain-Wall Transport in an Ultracold Bose Gas

Domain walls are carriers of spin transport whose controlled manipulation underlies a wide range of spintronic and information-processing technologies. Here we demonstrate tunable domain-wall transport in a weakly interacting nondegenerate ultracold Bose gas. We initialize a three-domain pseudo-spin-1/2 texture and observe spontaneous propagation of long-lived domain walls driven by exchange-mediated spin currents. By varying the orientation of the spin domains, we control the balance of spin currents across the walls and thereby tune their trajectories, including reversals of the initial direction of motion. Measurements reveal a crossover from an exchange-stabilized regime, in which coherent spin-exchange collisions suppress wall motion, to a diffusion-dominated regime characterized by rapid transport at thermal velocities. Numerical solutions of a quantum Boltzmann equation reproduce the observed dynamics and identify transverse phase gradients as an important control parameter governing domain-wall propagation. These results establish coherence and phase engineering as tools for programming spin transport in ultracold gases and provide a route toward controllable domain-wall dynamics in atomtronic systems.

cond-mat.quant-gas↗

arXiv2026

Symplectic Hopf Insulator: Delicate Topology in Bosonic Bogoliubov-de Gennes Systems

Recent advances in topological phases have highlighted the role of symplectic (Krein-space) topology in the classification of bosonic Bogoliubov-de Gennes (BBdG) systems. In this work, we construct a BBdG realization of Hopf topology, which we dub the symplectic Hopf insulator, starting from a microscopic Bose-Hubbard generalization of the Moore-Ran-Wen model with weak on-site interactions treated within a Bogoliubov approximation. The resulting BBdG system admits a symplectic Hopf invariant, which we show to be integer-quantized for isolated bands. We establish that this topology is intrinsically delicate, requiring exactly two bosonic modes per unit cell, while remaining robust against weak interactions over a range of mass parameters. Upon terminating the three-dimensional insulator at a boundary, we find topologically protected in-gap surface states at finite excitation energy, whose protection is itself delicate. Our results establish the symplectic Hopf insulator as a robust yet delicate topological phase in weakly interacting bosonic systems lying beyond the tenfold-way classification.

cond-mat.mes-hall↗

arXiv2005

Achievement of Quantum Degeneracy in a Na-QUIC trap in Brazil: an in situ observation

Using a system composed of a Quadrupole and Ioffe Configuration (QUIC) trap loaded from a slowed atomic beam, we have performed experiments to observe the Bose-Einstein Condensation of Na atoms. In order to obtain the atomic distribution in the trap, we use an in situ out of resonance absorption image through a probe beam, to determine temperature and density. The phase space density (D) is calculated using the density profile and the temperature. We have followed D as a function of the final evaporation frequency. The results show that at 1.65 MHz we crossed the value for D expected to correspond to the critical point to start de Bose-Condensation of the sample. Due to the low number of atoms remaining in the trap at the critical point, the interaction produces minor effects and therefore an ideal gas model explains well the observations. We analyze the obtained low number in terms of efficiency of evaporation. The utility of an in situ detection is illustrated by measuring the harmonic gas pressure of the trapped gas in the route to condensation.

cond-mat.other↗

arXiv2012

Open Quantum Systems. An Introduction

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions.

quant-ph↗

arXiv2013

Anderson's Orthogonality Catastrophe for One-dimensional Systems

We derive rigorously the leading asymptotics of the so-called Anderson integral in the thermodynamic limit for one-dimensional, non-relativistic, spin-less Fermi systems. The coefficient, $γ$, of the leading term is computed in terms of the S-matrix. This implies a lower and an upper bound on the exponent in Anderson's orthogonality catastrophe, $\tilde CN^{-\tildeγ}\leq \mathcal{D}_N\leq CN^{-γ}$ pertaining to the overlap, $\mathcal{D}_N$, of ground states of non-interacting fermions.

math-ph↗

arXiv2013

Hardy and Lieb-Thirring inequalities for anyons

We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $α\in [0,1]$ ranging from bosons ($α=0$) to fermions ($α=1$). We prove a (magnetic) Hardy inequality for anyons, which in the case that $α$ is an odd numerator fraction implies a local exclusion principle for the kinetic energy of such anyons. From this result, and motivated by Dyson and Lenard's original approach to the stability of fermionic matter in three dimensions, we prove a Lieb-Thirring inequality for these types of anyons.

math.SP↗

arXiv2013

Population trapping and inversion in ultracold Fermi gases by excitation of the optical lattice - Non-equilibrium Floquet-Keldysh description

A gas of ultracold interacting quantum degenerate Fermions is considered in a three dimensional optical lattice which is externally modulated in the fre- quency and the amplitude. This theoretical study utilizes the Keldysh formalism to account for the system being out of thermodynamical equilibrium. A dynamical mean field theory, extended to non-equilibrium, is presented to calculate characteristic quantities such as the local density of states and the non-equilibrium distribution function. A dynamics Franz-Keldysh splitting is found which accounts for the non-equilibrium modification of the underlying bandstructure. The found characteristic Floquet-fan like bandstructure accounts for the quantized nature of the effect over all frequency space.

cond-mat.quant-gas↗

arXiv2012

Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections.

cond-mat.quant-gas↗

arXiv2012

Spin superfluidity, coherent spin precession, and magnon BEC

Spin superfluidity, coherent spin precession, and magnon BEC are intensively investigated theoretically and experimentally nowadays. Meanwhile, clear definition and differentiation between these related phenomena is needed. It is argued that spin stiffness, which leads to existence of coherent spin precession and dissipationless spin supercurrents, is a necessary but not sufficient condition for spin superfluidity. The latter is defined as a possibility of spin transport on macroscopical distances with sufficiently large spin supercurrents. This possibility is realized at special topology of the magnetic-order-parameter space, such as, e.g., that in easy-plane antiferromagnets. It is argued that an arbitrarily chosen formal criterion for the existence of magnon BEC has no connection with conditions for observation of macroscopic dissipationless spin transport.

cond-mat.other↗

arXiv2013

Theories of Linear Response in BCS Superfluids and How They Meet Fundamental Constraints

We address the importance of symmetry and symmetry breaking on linear response theories of fermionic BCS superfluids. The linear theory of a noninteracting Fermi gas is reviewed and several consistency constraints are verified. The challenge to formulate linear response theories of BCS superfluids consistent with density and spin conservation laws comes from the presence of a broken U(1)$_{\textrm{EM}}$ symmetry associated with electromagnetism (EM) and we discuss two routes for circumventing this. The first route follows Nambu's integral-equation approach for the EM vertex function, but this method is not specific for BCS superfluids. We focus on the second route based on a consistent-fluctuation-of-the order-parameter (CFOP) approach where the gauge transformation and the fluctuations of the order parameter are treated on equal footing. The CFOP approach allows one to explicitly verify several important constraints: The EM vertex satisfies not only a Ward identity which guarantees charge conservation but also a $Q$-limit Ward identity associated with the compressibility sum rule. In contrast, the spin degrees of freedom associated with another U(1)$_z$ symmetry are not affected by the Cooper-pair condensation that breaks only the U(1)$_{\textrm{EM}}$ symmetry. As a consequence the collective modes from the fluctuations of the order parameter only couple to the density response function but decouple from the spin response function, which reflects the different fates of the two U(1) symmetries in the superfluid phase. Our formulation lays the ground work for application to more general theories of BCS-Bose Einstein Condensation crossover both above and below $T_c$.

cond-mat.supr-con↗

arXiv2013

Vortex molecules in Bose-Einstein condensates

Stable vortex dimers are known to exist in coherently coupled two component Bose-Einstein condensates (BECs). We construct stable vortex trimers in three component BECs and find that the shape can be controlled by changing the internal coherent (Rabi) couplings. Stable vortex N-omers are also constructed in coherently coupled N-component BECs. We classify all possible N-omers in terms of the mathematical graph theory. Next, we study effects of the Rabi coupling in vortex lattices in two-component BECs. We find how the vortex lattices without the Rabi coupling known before are connected to the Abrikosov lattice of integer vortices with increasing the Rabi coupling. In this process, vortex dimers change their partners in various ways at large couplings. We then find that the Abrikosov lattices are robust in three-component BECs.

cond-mat.quant-gas↗

arXiv2013

Precursor phenomena of nucleations of quantized vortices in the presence of a uniformly moving obstacle in Bose-Einstein condensates

We investigate excitations and fluctuations of Bose-Einstein condensates in a two-dimensional torus with a uniformly moving Gaussian potential by solving the Gross-Pitaevskii equation and the Bogoliubov equation. The energy gap $Δ$ between the current-flowing metastable state (that reduces to the ground state for sufficiently slowly-moving potential) and the first excited state vanishes when the moving velocity $v$ of the potential approaches a critical velocity v_c(>0). We find a scaling law $Δ\propto (1-|v|/v_c)^{1/4}$, which implies that a characteristic time scale diverges toward the critical velocity. Near the critical velocity, we show that low-energy local density fluctuations are enhanced. These behaviors can be regarded as precursor phenomena of the vortex nucleation.

cond-mat.quant-gas↗

arXiv2013

Vortex polygons and their stabilities in Bose-Einstein condensates and field theory

We study vortex polygons and their stabilities in miscible two-component Bose-Einstein condensates, and find that vortex polygons are stable for the total circulation $Q \leq 5$, metastable for $Q = 6$, and unstable for $Q \geq 7$. As a related model in high-energy physics, we also study the vortex polygon of the baby-Skyrme model with an anti-ferromagnetic potential term, and compare both results.

cond-mat.quant-gas↗

arXiv2012

Dynamics of one-dimensional tight-binding models with arbitrary time-dependent external homogeneous fields

The exact propagators of two one-dimensional systems with time-dependent external fields are presented by following the path-integral method. It is shown that the Bloch acceleration theorem can be generalized to the impulse-momentum theorem in quantum version. We demonstrate that an evolved Gaussian wave packet always keeps its shape in an arbitrary time-dependent homogeneous driven field. Moreover, that stopping and accelerating of a wave packet can be achieved by the pulsed field in a diabatic way.

quant-ph↗

arXiv2013

Excitons and Cavity Polaritons for Optical Lattice Ultracold Atoms

Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of geometries and dimensionality. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties. Even the formation of molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.

cond-mat.quant-gas↗

arXiv2013

Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit

We present a detailed analysis of the contribution of small-angle Nambu-Goldstone boson (phonon) collisions to the shear viscosity, $η$, in a superfluid atomic Fermi gas close to the unitarity limit. We show that the experimental values of the shear viscosity coefficient to entropy ratio, $η/s$, obtained at the lowest reached temperature can be reproduced assuming that phonons give the leading contribution to $η$. The phonon contribution is evaluated considering $1 \leftrightarrow 2$ processes and taking into account the finite size of the experimental system. In particular, for very low temperatures, $T \lesssim 0.1 T_F$, we find that phonons are ballistic and the contribution of phonons to the shear viscosity is determined by the processes that take place at the interface between the superfluid and the normal phase. This result is independent of the detailed form of the phonon dispersion law and leads to two testable predictions: the shear viscosity should correlate with the size of the optical trap and it should decrease with decreasing temperature. For higher temperatures the detailed form of the phonon dispersion law becomes relevant and, within our model, we find that the experimental data for $η/s$ can be reproduced assuming that phonons have an anomalous dispersion law.

cond-mat.quant-gas↗

arXiv2013

Superfluidity and collective modes in Rashba spin-orbit coupled Fermi gases

We present a theoretical study of the superfluidity and the corresponding collective modes in two-component atomic Fermi gases with s-wave attraction and synthetic Rashba spin-orbit coupling. The general effective action for the collective modes is derived from the functional path integral formalism. By tuning the spin-orbit coupling from weak to strong, the system undergoes a crossover from an ordinary BCS/BEC superfluid to a Bose-Einstein condensate of rashbons. We show that the properties of the superfluid density and the Anderson-Bogoliubov mode manifest this crossover. At large spin-orbit coupling, the superfluid density and the sound velocity become independent of the strength of the s-wave attraction. The two-body interaction among the rashbons is also determined. When a Zeeman field is turned on, the system undergoes quantum phase transitions to some exotic superfluid phases which are topologically nontrivial. For the two-dimensional system, the nonanalyticities of the thermodynamic functions and the sound velocity across the phase transition are related to the bulk gapless fermionic excitation which causes infrared singularities. The superfluid density and the sound velocity behave nonmonotonically: they are suppressed by the Zeeman field in the normal superfluid phase, but get enhanced in the topological superfluid phase. The three-dimensional system is also studied.

cond-mat.quant-gas↗