Up to date, the life time of experimentally demonstrated entangled states has been limited, due to their fragility under decoherence and dissipation. Therefore, they are created under strict isolation conditions. In contrast, new approaches harness the coupling of the system to the environment, which drives the system into the desired state. Following these ideas, we present a robust method for generating steady state entanglement between two distant atomic ensembles. The proposed scheme relies on the interaction of the two atomic systems with the common vacuum modes of the electromagnetic field which act as an engineered environment. We develop the theoretical framework for two level systems including dipole-dipole interactions and complement these results by considering the implementation in multi-level ground states.
We investigate the steady-state photon-number squeezing and quantum entanglement in a network of nondegenerate optical parametric oscillators (NOPOs). We treat each NOPO with Shen's Raman laser model, whose lasing mode provides a photon-number-squeezed state. Two dissipatively coupled NOPOs satisfy Hillery-Zubairy's $HZ1$ entanglement criterion if they are pumped far above the threshold and the dissipative coupling is sufficiently larger than the NOPO cavity loss.
We study the asymptotic entanglement of three identical qubits under the action of a Markovian open system dynamics that does not distinguish them. We show that by adding a completely depolarized qubit to a special class of two qubit states, by letting them reach the asymptotic state and by finally eliminating the added qubit, can provide more entanglement than by direct immersion of the two qubits within the same environment.
Non-Gaussian continuous variable states play a central role both in the foundations of quantum theory and for emergent quantum technologies. In particular, "cat states", i.e., two-component macroscopic quantum superpositions, embody quantum coherence in an accessible way and can be harnessed for fundamental tests and quantum information tasks alike. Degenerate optical parametric oscillators can naturally produce single-mode cat states and thus represent a promising platform for their realization and harnessing. We show that a dissipative coupling between degenerate optical parametric oscillato…
We show that two, non interacting, infinitely long spin chains can become globally entangled at the mesoscopic level of their fluctuation operators through a purely noisy microscopic mechanism induced by the presence of a common heat bath. By focusing on a suitable class of mesoscopic observables, the behaviour of the dissipatively generated quantum correlations between the two chains is studied as a function of the dissipation strength and bath temperature.
We present a scheme for dissipatively generating maximal entanglement in a heralded manner. Our setup requires incoherent interactions with two thermal baths at different temperatures, but no source of work or control. A pair of $(d+1)$-dimensional quantum systems is first driven to an entangled steady state by the temperature gradient, and maximal entanglement in dimension $d$ can then be heralded via local filters. We discuss experimental prospects considering an implementation in superconducting systems.
We show that macroscopic thermodynamical properties - such as functions of internal energy and magnetization - can detect quantum entanglement in solids at nonzero temperatures in the thermodynamical limit. We identify the parameter regions (critical values of magnetic field and temperature) within which entanglement is witnessed by these thermodynamical quantities.
We elucidate the relationship between Schrödinger-cat-like macroscopicity and geometric entanglement, and argue that these quantities are not interchangeable. While both properties are lost due to decoherence, we show that macroscopicity is rare in uniform and in so-called random physical ensembles of pure quantum states, despite possibly large geometric entanglement. In contrast, permutation-symmetric pure states feature rather low geometric entanglement and strong and robust macroscopicity.
Universidade Federal de São Carlos（圣卡洛斯联邦大学）；Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Stockholm University（斯德哥尔摩大学）；California Institute of Technology（加州理工学院）；Université Côte d’Azur（蔚蓝海岸大学）；CNRS, Institut de Physique de Nice（法国国家科学研究中心尼斯物理研究所）
We propose a scheme to dissipatively produce steady-state entanglement in a two-qubit system, via an interaction with a bosonic mode. The system is driven into a stationary entangled state, while we compensate the mode dissipation by injecting energy via a coherent pump field. We also present a scheme which allows us to adiabatically transfer all the population to the desired entangled state. The dynamics leading to the entangled state in these schemes can be understood in analogy with electromagnetically induced transparency (EIT) and stimulated Raman adiabatic passage (STIRAP), respectively.
A new mechanism is proposed for dissipatively preparing maximal Bell entangled state of two atoms in an optical cavity. This scheme integrates the spontaneous emission, the light shift of atoms in the presence of dispersive microwave field, and the quantum Zeno dynamics induced by continuous coupling, to obtain a unique steady state irrespective of initial state. Even for a large cavity decay, a high-fidelity entangled state is achievable at a short convergence time, since the occupation of cavity mode is inhibited by the Zeno requirement. Therefore, a low single-atom cooperativity $C=g^2/(κγ)…
Recently, there have been several suggestions that weak Kerr nonlinearity can be used for generation of macroscopic superpositions and entanglement and for linear optics quantum computation. However, it is not immediately clear that this approach can overcome decoherence effects. Our numerical study in this paper shows that nonlinearity of weak strength could be useful for macroscopic entanglement generation and quantum gate operations in the presence of decoherence. We suggest specific values for real experiments based on our analysis. Our discussion shows that the generation of macroscopic e…
We show how the spatial macroscopic entanglement equivalent to the off diagonal long range order (ODLRO) implies the Meissner effect and flux quantisation for a superconductor. It is argued by analogy with superconductors that the Higgs field must also be entangled in the same way. Internal (spin) entanglement is shown to be irrelevant within this context, although it can of course also be computed.
Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space - like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past. This novel Macro - Macro paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N=10^5 particles. Crucial experimental issues as the violation of Bell's inequalities by the Macro - Macro system are considered.
We propose and analyse a practically implementable scheme to generate macroscopic entanglement of a Bose-Einstein condensate in a micro-magnetic trap magnetically coupled to a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupled with the magnetic trap to generate macroscopic entanglement. Our scheme also provides a platform to realise interferometry of entangled atoms through the Bose-Einstein condensate and to explore physics at the quantum-classical interface.
We discuss the generation of a macroscopic entangled state in a single atom cavity-QED system. The three-level atom in a cascade configuration interacts dispersively with two classical coherent fields inside a doubly resonant cavity. We show that a macroscopic entangled state between these two cavity modes can be generated under large detuning conditions. The entanglement persists even under the presence of cavity losses.
What can we learn about entanglement between individual particles in macroscopic samples by observing only the collective properties of the ensembles? Using only a few experimentally feasible collective properties, we establish an entanglement measure between two samples of spin-1/2 particles (as representatives of two-dimensional quantum systems). This is a tight lower bound for the average entanglement between all pairs of spins in general and is equal to the average entanglement for a certain class of systems. We compute the entanglement measures for explicit examples and show how to genera…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems with a fluctuating particle number. To access the quality of the verified entanglement, the operational measure of the entanglement visibility is introduced. As an example, we perform an analytical characterization of quantum systems composed of interacting harmonic oscillators and witness the entanglement via energy measurements. Our analysis shows that the de…
We investigate the lifetime of macroscopic entanglement under the influence of decoherence. For GHZ-type superposition states we find that the lifetime decreases with the size of the system (i.e. the number of independent degrees of freedom) and the effective number of subsystems that remain entangled decreases with time. For a class of other states (e.g. cluster states), however, we show that the lifetime of entanglement is independent of the size of the system.
Using two different criteria for continuous variable systems we demonstrated that pump and probe beams became quantum correlated in a situation of Electromagnetically Induced Transparency in a sample of Rb atoms. Our result combines two important features for practical implementations in the field of quantum information processing. Namely, we proved the existence of entanglement between two macroscopic light beams, and this entanglement is intrinsically associated to a strong coherence in an atomic medium.
We investigate macroscopic entanglement of quantum states in quantum computers, where we say a quantum state is entangled macroscopically if the state has superposition of macroscopically distinct states. The index $p$ of the macroscopic entanglement is calculated as a function of the step of the computation, for Grover's quantum search algorithm and Shor's factoring algorithm. It is found that whether macroscopically entangled states are used or not depends on the numbers and properties of the solutions to the problem to be solved. When the solutions are such that the problem becomes hard in …
It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical entanglement. This paper presents a simple example, including a way in which the system can be measured to violate Bell's inequalities. This classical simulation of a quantum system allows us to visualize entanglement and also helps us to see what aspects of quantum mechanical systems are truly nonclassical.
Can entanglement and the quantum behavior in physical systems survive at arbitrary high temperatures? In this Letter we show that this is the case for a electromagnetic field mode in an optical cavity with a movable mirror in a thermal state. We also identify two different dynamical regimes of generation of entanglement separated by a critical coupling strength.
Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment, where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser- and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04s at room temperature. Our system consists of two ensembles containing about 10^{12} atoms and …
We show a general approach for detecting genuine multipartite entanglement (GME) and partial inseparability in many-body-systems by means of macroscopic observables (such as the energy) only. We show that the obtained criteria, the "GME gap" and "the k-entanglement gap", detect large areas of genuine multipartite entanglement and partial entanglement in typical many body states, which are not detected by other criteria. As genuine multipartite entanglement is a necessary property for several quantum information theoretic applications such as e.g. secret sharing or certain kinds of quantum comp…
We investigate entanglement properties of mixtures of short-range spin-s dimer coverings in lattices of arbitrary topology and dimension. We show that in one spacial dimension nearest neighbour entanglement exists for any spin $s$. Surprisingly, in higher spatial dimensions there is a threshold value of spin $s$ below which the nearest neighbour entanglement disappears. The traditional "classical" limit of large spin value corresponds to the highest nearest neighbour entanglement that we quantify using the negativity.
We show that the generation of entanglement of two heavily macroscopic mirrors with masses of up to several kilograms are feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the Standard Quantum Limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and prov…
This paper summarises the results of our research on macroscopic entanglement in spin systems and free Bosonic gases. We explain how entanglement can be observed using entanglement witnesses which are themselves constructed within the framework of thermodynamics and thus macroscopic observables. These thermodynamical entanglement witnesses result in bounds on macroscopic parameters of the system, such as the temperature, the energy or the susceptibility, below which entanglement must be present. The derived bounds indicate a relationship between the occurrence of entanglement and the establish…
The Pancharatnam phase deficit is defined as the difference between the Pancharat- nam phase acquired by the global system and the sum of the Pancharatnam phases acquired by subsystems during local unitary evolutions. We show that a non-zero value of the Pancharatnam phase deficit for a composite quantum system can be a signature of quantum entanglement. In the context of macroscopic quantum systems, we illustrate how the Pancharatnam phase deficit can be used to detect macroscopically entangled states. In particular, we use the Pancharatnam phase deficit to detect the entanglement for macrosc…
We show that if the ground state entanglement exceeds the total entropy of a given system, then this system is in an entangled state. This is a universal entanglement witness that applies to any physical system and yields a temperature below which we are certain to find some entanglement. Our witness is then applied to generic bosonic and fermionic many body systems to derive the corresponding "critical" temperatures that have a very broad validity.
We investigate entanglement properties of a recently introduced class of macroscopic quantum superpositions in two-mode mixed states. One of the tools we use in order to infer the entanglement in this non-Gaussian class of states is the power to entangle a qubit system. Our study reveals features which are hidden in a standard approach to entanglement investigation based on the uncertainty principle of the quadrature variables. We briefly describe the experimental setup corresponding to our theoretical scenario and a suitable modification of the protocol which makes our proposal realizable wit…
We investigate entanglement between collective operators of two wave-packets of finite spectral bandwidth, in two different approximations of the Multimode Parametric-Down Conversion (MPDC) process: the pairwise and the one-to-all interaction patterns. For collective operators we choose the macroscopic amplitudes of each wave-packet defined by the Fourier Transform of their microscopic mode amplitudes. This approach intends, to respond to realistic experimental conditions, where measurements apparatuses may not resolve single microscopic mode amplitudes but rather the collective amplitude of t…
Quantum entanglement between two or more bipartite entities is a core concept in quantum information areas limited to microscopic regimes directly governed by Heisenberg uncertainty principle via quantum superposition, resulting in nondeterministic and probabilistic quantum features. Such quantum features cannot be generated by classical means. Here, a pure classical method of on-demand entangled light-pair generation is presented in a macroscopic regime via basis randomness. This conflicting idea of conventional quantum mechanics invokes a fundamental question about both classicality and quan…
Entanglement between macroscopically populated states can easily be created by combining a single photon and a bright coherent state on a beam-splitter. Motivated by the simplicity of this technique, we report on a method using displacement operations in the phase space and basic photon detections to reveal such an entanglement. We demonstrate through preliminary experimental results, that this eminently feasible approach provides an attractive way for exploring entanglement at various scales, ranging from one to a thousand photons. This offers an instructive viewpoint to gain insight into the…
Displaced single-photon entanglement is a simple form of optical entanglement, obtained by sending a photon on a beamsplitter and subsequently applying a displacement operation. We show that it can generate, through a momentum transfer in the pulsed regime, an optomechanical entangled state involving macroscopically distinct mechanical components, even if the optomechanical system operates in the single-photon weak coupling regime. We discuss the experimental feasibility of this approach and show that it might open up a way for testing unconventional decoherence models.
We investigate how two spatially separated qubits coupled to a common heat bath can be entangled by purely dissipative dynamics. We identify a dynamical time scale associated with the lifetime of the dissipatively generated entanglement and show that it can be much longer than either the typical single-qubit decoherence time or the time scale on which a direct exchange interaction can entangle the qubits. We give an approximate analytical expression for the long-time evolution of the qubit concurrence and propose an ion trap scheme in which such dynamics should be observable.
We propose a deterministic scheme for establishing hybrid Einstein-Podolsky-Rosen (EPR) entanglement channel between a macroscopic mechanical oscillator and a magnon mode in a distant yttrium-iron-garnet (YIG) sphere across about ten gigahertz of frequency difference. The system consists of a driven electromechanical cavity which is unidirectionally coupled to a distant electromagnonical cavity inside which a YIG sphere is placed. We find that far beyond the sideband-resolved regime in the electromechanical subsystem, stationary phonon-magnon EPR entanglement can be achieved. This is realized …
The question whether Quantum Mechanics describes all aspects of both the micro-world of elementary particles and living organisms adequately is still open. A Bell inequality test without locality and detection loopholes will deliver the answer when applied to macroscopic systems. Here we show that an experimentally feasible loophole-free Bell test is possible using only multi-photon polarization entanglement and linear optics. We apply a preselection protocol which produces genuine macroscopic superpositions and entanglement, thus eliminating postselection and dark counts. Such superpositions …
Macroscopic entanglement distribution with atomic ensembles
East China Normal University（华东师范大学）；Federal Research Center of Problems of Chemical Physics and Medicinal Chemistry RAS（俄罗斯科学院化学物理与医药化学问题联邦研究中心）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）；New York University Shanghai（纽约大学上海分校）；Department of Physics, New York University（纽约大学物理系）
We propose a mechanism where high entanglement between very distant boundary spins is generated by suddenly connecting two long Kondo spin chains. We show that this procedure provides an efficient way to route entanglement between multiple distant sites. We observe that the key features of the entanglement dynamics of the composite spin chain are remarkably well described using a simple model of two singlets, each formed by two spins. The proposed entanglement routing mechanism is a footprint of the emergence of a Kondo cloud in a Kondo system and can be engineered and observed in varied physi…
Prospects for reaching persistent entanglement between two spatially separated atomic Bose-Einstein condensates are outlined. The system set-up comprises of two condensates loaded in an optical lattice, which, in return, is confined within a high-Q optical resonator. The system is driven by an external laser that illuminates the atoms such that photons can scatter into the cavity. In the superradiant phase a cavity field is established and we show that the emerging cavity mediated interactions between the two condensates is capable of entangling them despite photon losses. This macroscopic ato…
One of the main ingredients in most quantum information protocols is a reliable source of two entangled systems. Such systems have been generated experimentally several years ago for light but has only in the past few years been demonstrated for atomic systems. None of these approaches however involve two atomic systems situated in separate environments. This is necessary for the creation of entanglement over arbitrary distances which is required for many quantum information protocols such as atomic teleportation. We present an experimental realization of such distant entanglement based on an …
Explaining how microscopic entities collectively produce macroscopic phenomena is a fundamental goal of many-body physics. Theory predicts that large-scale entanglement is responsible for exotic macroscopic phenomena, but observation of entangled particles in naturally occurring systems is extremely challenging. Synthetic quantum systems made of atoms in optical lattices have been con- structed with the goal of observing macroscopic quantum phenomena with single-atom resolution. Serious challenges remain in producing and detecting long-range quantum correlations in these systems, however. Here…
In the Schrödinger-cat gedanken experiment a cat is in a quantum superposition of two macroscopically distinct states, alive and dead.The paradoxical interpretation of quantum mechanics is that the cat is not in one state or the other, alive or dead, immediately prior to its measurement. Because of this apparent defiance of macroscopic reality, quantum superpositions of states macroscopically distinct have generated much interest. Here we address the issue of proving a contradiction with macroscopic reality objectively, through the testable predictions of quantum mechanics. We consider the pre…
We show that the optomechanical coupling between an optical cavity mode and the two movable cavity end mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology.
The multiphoton quantum superposition generated by a quantum-injected optical parametric amplifier (QI-OPA) seeded by a single-photon belonging to an EPR entangled pair is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The effect can be greatly enhanced if the mirror is part of a cavity structure or is used within an optical interferometer. The overall process will realize an Entangled Macroscopic Quantum Superposition involving a ''microscopic'' singe-photon state of polarization and the coherent ''macroscopic'' displacement of the BEC structure acting in space-l…
We study optomechanical entanglement between an optical cavity field and a movable mirror coupled to a non-Markovian environment. The non-Markovian quantum state diffusion (NMQSD) approach and the non-Markovian master equation are shown to be useful in investigating the entanglement generation between the cavity field and the movable mirror. The simple model presented in this paper demonstrates several interesting properties of optomechanical entanglement that are associated with environment memory effects. It is evident that the effective environment central frequency can be used to modulate …
This study is aimed at investigating the feasibility of generating quantum entanglement between macroscopic mechanical mirrors in optomechanical systems while under continuous measurement and feedback control. We carefully derive a covariance matrix for mechanical mirrors in a steady state, employing the Kalman filtering problem with an assumed dominant cavity photon dissipation, such that the common and differential modes of the mirrors are squeezed by the action of measuring the output light beams. We demonstrate that entanglement between the mechanical mirrors is generated when the states o…
We address the presence of bound entanglement in strongly-interacting spin systems at thermal equilibrium. In particular, we consider thermal graph states composed of an arbitrary number of particles. We show that for a certain range of temperatures no entanglement can be extracted by means of local operations and classical communication, even though the system is still entangled. This is found by harnessing the independence of the entanglement in some bipartitions of such states with the system's size. Specific examples for one- and two-dimensional systems are given. Our results thus prove th…
Does bound entanglement naturally appear in quantum many-body systems? We address this question by showing the existence of bound-entangled thermal states for harmonic oscillator systems consisting of an arbitrary number of particles. By explicit calculations of the negativity for different partitions, we find a range of temperatures for which no entanglement can be distilled by means of local operations, despite the system being globally entangled. We offer an interpretation of this result in terms of entanglement-area laws, typical of these systems. Finally, we discuss generalizations of thi…
We investigate duality in entanglement of a bipartite multi-photon system generated from a coherent state of light. The system can exhibit polarization entanglement if the two parts are distinguished by their parity, or parity entanglement if the parts are distinguished by polarization. It was shown in [PRL 110, 140404 (2013)] that this phenomenon can be exploited as a method to test indistinguishability of two particles and it was conjectured that one can also test indistinguishability of macroscopic systems. We propose a setup to test this conjecture. Contrary to the previous studies using t…
We consider a Bell-like inequality performed using various instances of multi-photon entangled states to demonstrate that losses occurring after the unitary transformations used in the nonlocality test can be counteracted by enhancing the "size" of such entangled states. In turn, this feature can be used to overcome detection inefficiencies affecting the test itself: a slight increase in the size of such states, pushing them towards a more "macroscopic" form of entanglement, significantly improves the state robustness against detection inefficiency, thus easing the closing of the detection loo…
We investigate dynamics of an optomechanical system under the Non-Markovian environment. In the weak optomechanical single-photon coupling regime, we provide an analytical approach fully taking into account the non-Markovian memory effects. When the cavity-bath coupling strength crosses a certain threshold, an oscillating memory state for the classical cavity field (called bound state) is formed. Due to the existence of the non-decay optical bound state, a nonequilibrium optomechanical thermal entanglement is preserved even without external driving laser. Our results provide a potential usage …
Entangled coherent states, which can in principle be created using strong Kerr non-linearities, allow the violation of Bell inequalities for very coarse-grained measurements. This seems to contradict a recent conjecture that observing quantum effects in macroscopic systems generally requires very precise measurements. However, here we show that both the creation of the required states and the required measurements rely on being able to control the phase of the necessary Kerr-nonlinearity based unitary operations with extreme precision. This lends support to the idea that there is a general pri…
We study an isolated, perfectly reflecting, mirror illuminated by an intense laser pulse. We show that the resulting radiation pressure efficiently entangles a mirror vibrational mode with the two reflected optical sideband modes of the incident carrier beam. The entanglement of the resulting three-mode state is studied in detail and it is shown to be robust against the mirror mode temperature. We then show how this continuous variable entanglement can be profitably used to teleport an unknown quantum state of an optical mode onto the vibrational mode of the mirror.
Quantum entanglement in mechanical systems is not only a key signature of macroscopic quantum effects, but has wide applications in quantum technologies. Here we proposed an effective approach for creating strong steady-state entanglement between two directly coupled mechanical oscillators (or a mechanical oscillator and a microwave resonator) in a modulated optomechanical system. The entanglement is achieved by combining the processes of a cavity cooling and the two-mode parametric interaction, which can surpass the bound on the maximal stationary entanglement from the two-mode parametric int…
In this paper I intend to show that macroscopic entanglement is possible at high temperatures. I analyze multipartite entanglement produced by the $η$ pairing mechanism which features strongly in the fermionic lattice models of high $T_c$ superconductivity. This problem is shown to be equivalent to calculating multipartite entanglement in totally symmetric states of qubits. I demonstrate that we can conclusively calculate the relative entropy of entanglement within any subset of qubits in an overall symmetric state. Three main results then follow. First, I show that the condition for supercond…
