The entanglement between occupation-numbers of different single particle basis states depends on coupling between different single particle basis states in the second-quantized Hamiltonian. Thus in principle, interaction is not necessary for occupation-number entanglement to appear. However, in order to characterize quantum correlation caused by interaction, we use the eigenstates of the single-particle Hamiltonian as the single particle basis upon which the occupation-number entanglement is defined. Using the proper single particle basis, we discuss occupation-number entanglement in important eigenstates, especially ground states, of systems of many identical particles. The discussions on Fermi systems start with Fermi gas, Hatree-Fock approximation, and the electron-hole entanglement in excitations. The entanglement in a quantum Hall state is quantified as -fln f-(1-f)ln(1-f), where f is the proper fractional part of the filling factor. For BCS superconductivity, the entanglement is a function of the relative momentum wavefunction of the Cooper pair, and is thus directly related to the superconducting energy gap. For a spinless Bose system, entanglement does not appear in the Hatree-Gross-Pitaevskii approximation, but becomes important in the Bogoliubov theory.
Condensed matter systems are potential candidates to realize the integration of quantum information circuits. Surface phonon polariton (SPhP) is a special propagation mode in condensed matter systems. We present an investigation on the entanglement of SPhP modes. The entangled pairs are generated from entangled photons injected to the system. Quantum performances of entangled SPhPs are investigated by using the interaction Hamiltonian and the perturbation theory. The wave mechanics approach is taken to describe the coupling process as a comparison. Finally, the correlation of system is examine…
We model recent experiments on living sulphur bacteria interacting with quantised light, using the Dicke model. The strong coupling achieved between the bacteria and the light indicates that during the experiment the bacteria (treated as dipoles) and the quantized light are entangled. The vacuum Rabi splitting, which was measured in the experiment for a range of different parameters, can be used as an entanglement witness.
We analyze the optomechanics-like properties of a Bose-Einstein condensate (BEC) trapped inside an optical resonator and driven by both a classical and a quantized light field. We find that this system exhibits a nature of role reversal between the matter-wave field and the quantized light field. As a result, the matter wave field now plays the role of the quantized light field, and the quantized light field behaves like a movable mirror, in contrast to the familiar situation in BEC-based cavity optomechanics [Brennecke et al., Science 322, 235 (2008); Murch et al., Nat. Phys. 4, 561 (2008)]. …
These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular Matrix Product States (MPS) and Projected Entangled Pair States (PEPS), which provide an efficient description of many-body states based on their entanglement structure; both numerical and analytical aspects of tensor networks are being covered. The notes close with a brief introduction to quantum complexity, which allows to assess the limitations to our ability …
The electronic entanglement between two free atoms initially at rest is obtained including the effects of photon recoil, for the case when quantum dispersion can be neglected during the atomic excited-state lifetime. Different from previous treatments using common or statistically independent reservoirs, a continuous transition between these limits is observed, that depends on the inter-atomic distance and degree of localization. The occurrence of entanglement sudden death and birth as predicted here deviates from the case where the inter-atomic distance is treated classically by a static valu…
Quantum correlations between two neighbor atoms are studied. It is assumed that one atomic system comprises a single auto-ionizing level and the other atom does not contain any auto-ionizing level. The excitation of both atoms is achieved by the interaction with the same mode of the quantized field. It is shown that the long-time behavior of two atoms exhibits quantum correlations even when the atoms do not interact directly. This can be shown using the optical excitation of the neighbor atom. Also a measure of entanglement of two atoms can be applied after reduction of the continuum to two le…
We observe that the many-body eigenstates of any quadratic, fermionic Hamiltonian with sublattice symmetry have quantized entanglement entropies between the sublattices: the entanglement comes in multiple singlets. Moreover, such systems always have a ground state that is maximally entangled between the two sublattices. In fact we also show that under the same assumptions there always exists a (potentially distinct) basis of energy eigenstates that do not conserve the particle number in which each energy eigenstate is maximally entangled between the sublattices. No additional properties, such …
This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for entanglement used for this analysis. A selection of results from this research is given and proposed as evidence for the relevance of multipartite entanglement in this context. A constructive method for an SLOCC classification and quantification of multipartite qubit entanglement is outlined and results for convex roof extensions of the resulting measures are briefly …
We show how entanglement may be quantified in spin and cold atom many-body systems using standard experimental techniques only. The scheme requires no assumptions on the state in the laboratory and a lower bound to the entanglement can be read off directly from the scattering cross section of Neutrons deflected from solid state samples or the time-of-flight distribution of cold atoms in optical lattices, respectively. This removes a major obstacle which so far has prevented the direct and quantitative experimental study of genuine quantum correlations in many-body systems: The need for a full …
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated Rényi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discusse…
In this paper, we study the interaction between a moving $Λ$-type three-level atom and a single-mode cavity field in the presence of intensity-dependent atom-field coupling. After obtaining the state vector of the entire system explicitly, we study the nonclassical features of the system such as quantum entanglement, position-momentum entropic squeezing, quadrature squeezing and sub-Poissonian statistics. According to the obtained numerical results we illustrate that the squeezed period, the duration of entropy squeezing and the maximal squeezing can be controlled by choosing the appropriate n…
Quantum Electrodynamics may be formulated as a Quantum Field Theory , and also as relativistic quantum mechanics by introduction of the Feynman-Stueckelberg parameter. As stated by M. Srednicki ({\it Quantum Field Theory}, Cambridge University Press, Cambridge and New York, 2007), "\dots any relativistic quantum physics that can be treated in one formalism can also be treated in the other". Entanglement of electrons at macroscopic spacelike separation has been observed (B. Hensen {\it et al.}, Nature, $\bf{526}$, 2015, doi:10.1038.nature/15759), yet according to Quantum Field Theory is restric…
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter,…
Various lower- and higher-order nonclassical properties have been studied for two physical systems- (i) an optomechanical system composed of a Fabry-Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose-Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and highe…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence between the quantum information formalism of tensor networks (TN), in the case of projected entangled-pair states (PEPS) generalised to a second-quantized framework, and group field theory (GFT) states, and by showing how, in this quantum gravity approach, discrete spatial manifolds arise as entanglement patterns among quanta of space, having a dual representation…
We investigate some aspects of the dynamics and entanglement of bipartite quantum system (atom-quantized field), coupled to a third ``external" subsystem (quantized field). We make use of the Raman coupled model; a three-level atom in a lambda configuration interacting with two modes of the quantized cavity field. We consider the far off resonance limit, which allows the derivation of an effective Hamiltonian of a two-level atom coupled to the fields. We also make a comparison with the situation in which one of the modes is treated classically rather than prepared in a quantum field (coherent …
Second-quantized numerical simulations of tunable entanglement in quantum high harmonic generation
Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质与结构动力学研究所）；Center for Computational Quantum Physics, The Flatiron Institute（平顿研究院计算量子物理中心）；Technion - Israel Institute of Technology（以色列理工学院）
Photons may have homogeneous polarization and may carry quantized orbital angular momentum (OAM). Photon entanglement has been realized in various degrees of freedom such as polarization and OAM. Using a pair of orthogonally polarized states carrying opposite-handedness quantized OAMs could create "quantized" vector polarization states with space-variant polarization structures. It is thus possible to extend the polarization degree of freedom from two dimensional space to indefinite dimensional discrete Hilbert space. We present a class of vector-polarization entangled Bell states, which use t…
Quantum entanglement is a quantum mechanical phenomenon where the quantum state of a many-body system with many degrees of freedom cannot be described independently of the state of each body with a given degree of freedom, no matter how far apart in space each body is. Entanglement is not only considered a resource in quantum information but also believed to affect complex condensed matter systems. Detecting and quantifying multi-particle entanglement in a many-body system is thus of fundamental significance for both quantum information science and condensed matter physics. Here, we detect and…
Experiments witnessing the entanglement between two particles interacting only via the gravitational field have been proposed as a test whether gravity must be quantized. In the language of quantum information, a non-quantum gravitational force would be modeled by local operations with classical communication (LOCC), which cannot generate entanglement in an initially unentangled state. This idea is criticized as too constraining on possible alternatives to quantum gravity. We present a parametrized model for the gravitational interaction of quantum matter on a classical spacetime, inspired by …
Low dissipation, tunable coupling to other quantum systems, and unique features of phonons in the aspects of propagation, detection and others suggest the applications of quantized mechanical resonators in phonon-based quantum information processing (QIP) in a way different from their photonic counterpart. In this paper, we propose the first protocol of entanglement concentration for nonlocal phonons from quantized mechanical vibration. We combine the optomechanical cross-Kerr interaction with the Mach-Zehnder interferometer and, by means of twice optomechanical interactions and the photon ana…
Entanglement is widely considered the cornerstone of quantum information and an essential resource for relevant quantum effects, such as quantum teleportation, quantum cryptography, or the speed-up of quantum computing, as in Shor's algorithm. However, up to now, there is no general characterization of entanglement for many-body systems. In this sense, it is encouraging that quantum states connected by stochastic local operations assisted with classical communication (SLOCC), which perform probabilistically the same quantum tasks, can be collected into entanglement classes. Nevertheless, there…
We propose a nonlinear atom-optics experiment to create diffraction catastrophes threaded by quantized vortex skeletons in Bose-Einstein condensed matter waves. We show how atom-optical aberrations induced in trapped Bose-Einstein condensates evolve into specific caustic structures due to imperfect focusing. Vortex skeletons, whose cross-sections are staggered vortex lattices, are observed to nucleate inside the universal diffraction catastrophes. Our observations shed further light on the structure and dynamics of Bose-novae and suggest applications of matter wave diffraction catastrophes, in…
A method is developed for realizing entanglement and general second quantized fermionic and bosonic fields in the framework of the fermionic projector.
The paper focuses on aspects of the measurement problem introducing quantum states (q-states) for measured and measuring systems. The link between non-interacting and interacting quantum systems is first look at. For two independent partite systems logical sums A+B stand for non-interacting q-systems; while a direct product space AxB gathers interacting states. However this latter should support physical q-states with base states that do not separately belong to either A nor B; the latter correspond to bridge states, namely entangled states that can perform as links (bridges) between A+B and A…
We analyze the steady-state entanglement between Bose-Einstein condensate trapped inside an optical cavity with a moving end mirror (nanomechanical resonator) driven by a single mode laser. The quantized laser field mediates the interaction between the Bose-Einstein condensate and nanomechanical resonator. In particular, we study the influence of temperature on the entanglement of the coupled system, and note that the steady-state entanglement is fragile with respect to temperature.
Rather than an a priori arena in which events take place, space-time is a construction of our mind making possible a particular kind of ordering of events. As quantum entanglement is a property of states independent of classical distances, the notion of space and time has to be revised to represent the holistic interconnection of quanta. We also speculate about various forms of reprogramming, or reconfiguring, the propagation of information for multipartite statistics and in quantum field theory.
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
We calculate the entanglement of a generalized elliptical vortex formed by quantized radiation field, using Wigner quasiprobability distribution function for such states. We find a critical squeezing parameter above which the entanglement is less for higher vorticity, which is counter intuitive.
We introduce a new kind of Entanglement Witness which is appropriate for studying genuine multipartite entanglement in large systems. The witness operator has a form that fits naturally to quantum states represented by tensor networks. It opens up novel routes for investigating properties of condensed matter systems, and gives a new perspective to understand many-body quantum correlations. We illustrate the potential of this new operator with a GHZ state, and apply the method to a transverse Ising model with the well-known approach of Matrix Product States and Matrix Product Operators for a hu…
Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon
近年来，利用集体增强技术成功地实现了原子系综与单光子的纠缠[D. N. Matsukevich，\textit{et al.}，物理学评论快报。\textbf{95}，040405（2005）.]，其中原子内态和光子偏振态以非局域方式关联。在这里，我们通过实验阐明了在原子系综和光子系统中，也存在着与空间自由度有关的纠缠。讨论了远程原子系综之间高维纠缠的产生及其在凝聚态物理中的应用。
We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t=0. The feasibility of experimentally detecting this effect is discussed.
The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple geometric properties of "chiral" group $SU (N)\times SU(N)$ and is based on considering the stability subgroup of the initial state of the game. The explicit forms of neither the gate operator nor the payoff matrix are necessary.
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain measurements, and for entangled composite events. The role of the prospect and state entanglement is emphasized. Numerical modeling is presented for a two-mode Bose-condensed system of trapped atoms. The interference factor is calculated by invoking the channel-state duality.
Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge modes as their topological winding. In this work, we disc…
We present a simple calculation leading to the quantum gravitationally-induced decoherence of a spatial superposition of a massive object in the linear coupling regime. The point of this calculation is to illustrate that the gravitationally-induced collapse could be of the same origin as any other collapse, i.e. due to the entanglement between the system (here a massive object) and its environment (in this case gravity, but it could well be the electromagnetic or any other field). We then point out that, in some cases, one has to be careful when concluding that matter-wave interference of larg…
The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the two-qubit dissipative and dephasing models. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the system state space.
The entanglement between two atoms in a damping Jaynes-Cummings model is investigated with different decay coefficients of the atoms from the upper level to other levels under detuning between the atomic frequency and the quantized light field frequency. The results indicate that the larger the decay coefficient is, the more quickly the entanglement decays. The detuning enhances the entanglement's average value at long times. More importantly, the results show that the so-called sudden death effect can be avoided by enhancing the detuning or the decay coefficient.
