arXiv subjects

Maciej Lewenstein

Publications and source records attributed to Maciej Lewenstein.

At least 361 records · Page 20Linked to original sources

arXiv2011

Particle Counting Statistics of Time and Space Dependent Fields

The counting statistics give insight into the properties of quantum states of light and other quantum states of matter such as ultracold atoms or electrons. The theoretical description of photon counting was derived in the 1960s and was extended to massive particles more recently. Typically, the interaction between each particle and the detector is assumed to be limited to short time intervals, and the probability of counting particles in one interval is independent of the measurements in previous intervals. There has been some effort to describe particle counting as a continuous measurement, where the detector and the field to be counted interact continuously. However, no general formula applicable to any time and space dependent field has been derived so far. In our work, we derive a fully time and space dependent description of the counting process for linear quantum many-body systems, taking into account the back-action of the detector on the field. We apply our formalism to an expanding Bose-Einstein condensate of ultracold atoms, and show that it describes the process correctly, whereas the standard approach gives unphysical results in some limits. The example illustrates that in certain situations, the back-action of the detector cannot be neglected and has to be included in the description.

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arXiv2011

Gauge fields emerging from time reversal symmetry breaking for spin-5/2 fermions in a honeycomb lattice

We propose an experimentally feasible setup with ultracold alkaline earth atoms to simulate the dynamics of U(1) lattice gauge theories in 2+1 dimensions with a Chern-Simons term. To this end we consider the ground state properties of spin-5/2 alkaline earth fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin liquid state with $2π/3$ flux per plaquette, which spontaneously violates time reversal invariance. We demonstrate that due to the breaking of time reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge field dynamics. We discuss also properties of the lowest energy competing orders.

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arXiv2011

An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.

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arXiv2011

On structural physical approximations and entanglement breaking maps

Very recently a conjecture saying that the so-called structural physical approximations (SPAa) to optimal positive maps (optimal entanglement witnesses) give entanglement breaking (EB) maps (separable states) has been posed [J. K. Korbicz {\it et al.}, Phys. Rev. A {\bf 78}, 062105 (2008)]. The main purpose of this contribution is to explore this subject. First, we extend the set of entanglement witnesses (EWs) supporting the conjecture. Then, we ask if SPAs constructed from other than the depolarizing channel maps also lead to EB maps and show that in general this is not the case. On the other hand, we prove an interesting fact that for any positive map $Λ$ there exists an EB channel $Φ$ such that the SPA of $Λ$ constructed with the aid of $Φ$ is again an EB channel. Finally, we ask similar questions in the case of continuous variable systems. We provide a simple way of construction of SPA and prove that in the case of the transposition map it gives EB channel.

quant-ph↗

arXiv2011

A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces

Entanglement witnesses (EWs) constitute one of the most important entanglement detectors in quantum systems. Nevertheless, their complete characterization, in particular with respect to the notion of optimality, is still missing, even in the decomposable case. Here we show that for any qubit-qunit decomposable EW (DEW) W the three statements are equivalent: (i) the set of product vectors obeying \bra{e,f}W\ket{e,f}=0 spans the corresponding Hilbert space, (ii) W is optimal, (iii) W=Q^Γ with Q denoting a positive operator supported on a completely entangled subspace (CES) and Γstanding for the partial transposition. While, implications $(i)\Rightarrow(ii)$ and $(ii)\Rightarrow(iii)$ are known, here we prove that (iii) implies (i). This is a consequence of a more general fact saying that product vectors orthogonal to any CES in C^{2}\otimes C^{n} span after partial conjugation the whole space. On the other hand, already in the case of C^{3}\otimes C^{3} Hilbert space, there exist DEWs for which (iii) does not imply (i). Consequently, either (i) does not imply (ii), or (ii) does not imply (iii), and the above transparent characterization obeyed by qubit-qunit DEWs, does not hold in general.

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arXiv2011

Quantum simulation of frustrated magnetism in triangular optical lattices

Magnetism plays a key role in modern technology as essential building block of many devices used in daily life. Rich future prospects connected to spintronics, next generation storage devices or superconductivity make it a highly dynamical field of research. Despite those ongoing efforts, the many-body dynamics of complex magnetism is far from being well understood on a fundamental level. Especially the study of geometrically frustrated configurations is challenging both theoretically and experimentally. Here we present the first realization of a large scale quantum simulator for magnetism including frustration. We use the motional degrees of freedom of atoms to comprehensively simulate a magnetic system in a triangular lattice. Via a specific modulation of the optical lattice, we can tune the couplings in different directions independently, even from ferromagnetic to antiferromagnetic. A major advantage of our approach is that standard Bose-Einstein-condensate temperatures are sufficient to observe magnetic phenomena like Néel order and spin frustration. We are able to study a very rich phase diagram and even to observe spontaneous symmetry breaking caused by frustration. In addition, the quantum states realized in our spin simulator are yet unobserved superfluid phases with non-trivial long-range order and staggered circulating plaquette currents, which break time reversal symmetry. These findings open the route towards highly debated phases like spin-liquids and the study of the dynamics of quantum phase transitions.

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arXiv2011

Atom Counting in Expanding Ultracold Clouds

We study the counting statistics of ultracold bosonic atoms that are released from an optical lattice. We show that the counting probability distribution of the atoms collected at a detector located far away from the optical lattice can be used as a method to infer the properties of the initially trapped states. We consider initial superfluid and insulating states with different occupation patterns. We analyze how the correlations between the initially trapped modes that develop during the expansion in the gravitational field are reflected in the counting distribution. We find that for detectors that are large compared to the size of the expanded wave function, the long-range correlations of the initial states can be distinguished by observing the counting statistics. We consider counting at one detector, as well as the joint probability distribution of counting particles at two detectors. We show that using detectors that are small compared to the size of the expanded wave function, insulating states with different occupation patterns, as well as supersolid states with different density distributions can be distinguished.

quant-ph↗

arXiv2011

Tunable dipolar resonances and Einstein-de Haas effect in a Rb-87 atoms condensate

We study a spinor condensate of Rb-87 atoms in F = 1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in mF = 1 component we observe a significant transfer of atoms to other, initially empty Zeeman states exclusively due to dipolar forces. Because of conservation of a total angular momentum the atoms going to other Zeeman components acquire an orbital angular momentum and circulate around the center of the trap. This is a realization of Einstein-de Haas effect in a system of cold gases. We show that the transfer of atoms via dipolar interaction is possible only when the energies of the initial and the final sates are equal. This condition can be fulfilled utilizing a resonant external magnetic field, which tunes energies of involved states via the linear Zeeman effect. We found that there are many final states of different spatial density which can be tuned selectively to the initial state. We show a simple model explaining high selectivity and controllability of weak dipolar interactions in the condensate of Rb-87 atoms.

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arXiv2010

Bose-Hubbard model with occupation dependent parameters

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose-Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling the system features a phase-transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background -- instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with 2 particles per site is destroyed completely by particle-hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction, but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a 2D slab, localized along one spatial direction that is spontaneously chosen.

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arXiv2010

Complete devil's staircase and crystal--superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many meta-stable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization, and quasiexact numerical techniques (density-matrix renormalization group and infinite time evolving block decimation). We find that the complete devil's staircase -- an infinite sequence of crystal states existing at vanishing tunneling -- spreads to a succession of lobes similar to the Mott-lobes found in Bose--Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar two-dimensional models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long range (algebraic) correlations, opposed to models with nearest-neighbor tunneling which show exponential decay of correlations.

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arXiv2010

Fermion- and spin-counting in strongly correlated systems in and out of thermal equilibrium

Atom counting theory can be used to study the role of thermal noise in quantum phase transitions and to monitor the dynamics of a quantum system. We illustrate this for a strongly correlated fermionic system, which is equivalent to an anisotropic quantum XY chain in a transverse field, and can be realized with cold fermionic atoms in an optical lattice. We analyze the counting statistics across the phase diagram in the presence of thermal fluctuations, and during its thermalization when the system is coupled to a heat bath. At zero temperature, the quantum phase transition is reflected in the cumulants of the counting distribution. We find that the signatures of the crossover remain visible at low temperature and are obscured with increasing thermal fluctuations. We find that the same quantities may be used to scan the dynamics during the thermalization of the system.

quant-ph↗

arXiv2010

The ground state of binary systems with a periodic modulation of the linear coupling

We consider a quasi-one-dimensional two-component systm, described by a pair of Nonlinear Schrödinger/Gross-Pitaevskii Equations (NLSEs/GPEs), which are coupled by the linear mixing, with local strength $Ω$, and by the nonlinear incoherent interaction. We assume the self-repulsive nonlinearity in both components, and include effects of a harmonic trapping potential. The model may be realized in terms of periodically modulated slab waveguides in nonlinear optics, and in Bose-Einstein condensates too. Depending on the strengths of the linear and nonlinear couplings between the components, the ground states (GSs) in such binary systems may be symmetric or asymmetric. In this work, we introduce a periodic spatial modulation of the linear coupling, making $Ω$ an odd, or even function of the coordinate. The sign flips of $Ω(x)$ strongly modify the structure of the GS in the binary system, as the relative sign of its components tends to lock to the local sign of $Ω$. Using a systematic numerical analysis, and an analytical approximation, we demonstrate that the GS of the trapped system contains one or several kinks (dark solitons) in one component, while the other component does not change its sign. Final results are presented in the form of maps showing the number of kinks in the GS as a function of the system's parameters, with the odd/even modulation function giving rise to the odd/even number of the kinks. The modulation of $Ω(x)$ also produces a strong effect on the transition between states with nearly equal and strongly unequal amplitudes of the two components.

quant-ph↗

arXiv2010

Controlled hole doping of a Mott insulator of ultracold fermionic atoms

Considering a system of ultracold atoms in an optical lattice, we propose a simple and robust implementation of a quantum simulator for the homogeneous t-J model with a well-controlled fraction of holes x. The proposed experiment can provide valuable insight into the physics of cuprate superconductors. A similar scheme applied to bosons, moreover, allows one to investigate experimentally the subtle role of inhomogeneity when a system passes from one quantum phase to another.

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arXiv2010

Emerging Bosons with Three-Body Interactions from Spin-1 Atoms in Optical Lattices

We study two many-body systems of bosons interacting via an infinite three-body contact repulsion in a lattice: a pairs quasi-condensate induced by correlated hopping and the discrete version of the Pfaffian wavefunction. We propose to experimentally realise systems characterized by such interaction by means of a proper spin-1 lattice Hamiltonian: spin degrees of freedom are locally mapped into occupation numbers of emerging bosons, in a fashion similar to spin-1/2 and hardcore bosons. Such a system can be realized with ultracold spin-1 atoms in a Mott Insulator with filling-factor one. The high versatility of these setups allows us to engineer spin-hopping operators breaking the SU(2) symmetry, as needed to approximate interesting bosonic Hamiltonians with three-body hardcore constraint. For this purpose we combine bichromatic spin-independent superlattices and Raman transitions to induce a different hopping rate for each spin orientation. Finally, we illustrate how our setup could be used to experimentally realize the first setup, i.e. the transition to a pairs quasi-condensed phase of the emerging bosons. We also report on a route towards the realization of a discrete bosonic Pfaffian wavefunction and list some open problems to reach this goal.

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arXiv2010

Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices

Periodicity is one of the most fundamental structural characteristics of systems occurring in nature. The properties of these systems depend strongly on the symmetry of the underlying periodic structure. In solid state materials - for example - the static and transport properties as well as the magnetic and electronic characteristics are crucially influenced by the crystal symmetry. In this context, hexagonal structures play an extremely important role and lead to novel physics like that of carbon nanotubes or graphene. Here we report on the first realization of ultracold atoms in a spin-dependent optical lattice with hexagonal symmetry. We show how combined effects of the lattice and interactions between atoms lead to a forced antiferromagnetic Néel order when two spin-components localize at different lattice sites. We also demonstrate that the coexistence of two components - one Mott-insulating and the other one superfluid - leads to the formation of a forced supersolid. Our observations are consistent with theoretical predictions using Gutzwiller mean-field theory.

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arXiv2010

Disorder-Induced Order in Quantum XY Chains

We observe signatures of disorder-induced order in 1D XY spin chains with an external, site-dependent uni-axial random field within the XY plane. We numerically investigate signatures of a quantum phase transition at T=0, in particular an upsurge of the magnetization in the direction orthogonal to the external magnetic field, and the scaling of the block-entropy with the amplitude of this field. Also, we discuss possible realizations of this effect in ultra-cold atom experiments.

quant-ph↗

arXiv2010

Disordered quantum gases under control

When attempting to understand the role of disorder in condensed-matter physics, one faces severe experimental and theoretical difficulties and many questions are still open. Two of the most challenging ones, which have been debated for decades, concern the effect of disorder on superconductivity and quantum magnetism. Recent progress in ultracold atomic gases paves the way towards realization of versatile quantum simulators which will be useful to solve these questions. In addition, ultracold gases offer original situations and viewpoints, which open new perspectives to the field of disordered systems.

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arXiv2010

Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice

We propose to realize the anisotropic triangular-lattice Bose-Hubbard model with positive tunneling matrix elements by using ultracold atoms in an optical lattice dressed by a fast lattice oscillation. This model exhibits frustrated antiferromagnetism at experimentally feasible temperatures; it interpolates between a classical rotor model for weak interaction, and a quantum spin-1/2 $XY$-model in the limit of hard-core bosons. This allows to explore experimentally gapped spin liquid phases predicted recently [Schmied et al., New J. Phys. {\bf 10}, 045017 (2008)].

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