Recently, atomic ensemble and single photons were successfully entangled by using collective enhancement [D. N. Matsukevich, \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 040405(2005).], where atomic internal states and photonic polarization states were correlated in nonlocal manner. Here we experimentally clarified that in an ensemble of atoms and a photon system, there also exists an entanglement concerned with spatial degrees of freedom. Generation of higher-dimensional entanglement between remote atomic ensemble and an application to condensed matter physics are also discussed.
We study the ground-state entanglement and thermal entanglement in the hyperfine interaction of the lithium atom. We give the relationship between the entanglement and both temperature and external magnetic fields.
We replace time-averaged entanglement by ensemble-averaged entanglement and derive a simple expression for the latter. We show how to calculate the ensemble average for a two-spin system and for the Jaynes-Cummings model. In both cases the time-dependent entanglement is known as well so that one can verify that the time average coincides with the ensemble average.
A new approach to the measurement of gravitational fields with an equilibrium ensemble of ultra-cold alkali atoms confined in a cell of volume $V$ is investigated. The proposed model of the gravitational sensor is based on a variation of the density profile of the ensemble due to changing of the gravitational field. For measurement the atomic density variations of the ensemble the electromagnetically induced transparency method is used.
We present experimental demonstration of quadrature and polarization entanglement generated via the interaction between a coherent linearly polarized field and cold atoms in a high finesse optical cavity. The non linear atom-field interaction produces two squeezed modes with orthogonal polarizations which are used to generate a pair of non separable beams, the entanglement of which is demonstrated by checking the inseparability criterion for continuous variables recently derived by Duan et al. [Phys. Rev. Lett. 84, 2722 (2000)] and calculating the entanglement of formation [Giedke et al., Phys…
With the mechanism of pairwise scattering of photons between two atoms, we propose a novel scheme to highly entangle the motional state between two ultracold neutral atoms by a single photon scattering and detection. Under certain conditions, it is shown that an arbitrary amount of entanglement can be obtained with this scheme.
With the reliance in the processing of quantum information on a cold trapped ion, we analyze the entanglement entropy in the ion-field interaction with pair cat states. We investigate a long-living entanglement allowing the instantaneous position of the center-of-mass motion of the ion to be explicitly time dependent. An analytic solution for the system operators is obtained. We show that different nonclassical effects arise in the dynamics of the population inversion, depending on the initial states of the vibrational motion. We study in detail the entanglement degree and demonstrate how the …
We propose an experimentally feasible scheme to generate nonmaximal entanglement between two atomic ensembles. The degree of entanglement is readily tunable. The scheme involves laser manipulation of atomic ensembles, adjustable quarter- and half-wave plates, beam splitter, polarizing beam splitters, and single-photon detectors, and well fits the status of the current experimental technology. Finally we use the nonmaximally entangled state of ensembles to demonstrate quantum nonlocality by detecting the Clauser-Horne-Shimony-Holt inequality.
Cold atomic ensembles can mediate the generation of entanglement between pairs of photons. Photons with specific directions of propagation are detected, and the entanglement can reside in any of the degrees of freedom that describe the whole quantum state of the photons: polarization, spatial shape or frequency. We show that the direction of propagation of the generated photons determines the spatial quantum state of the photons and therefore, the amount of entanglement generated. When photons generated in different directions are combined, this spatial distinguishing information can degrade t…
We propose an experimentally feasible scheme to demonstrate quantum nonlocality, using Greenberger-Horne-Zeilinger (GHZ) and $W$ entanglement between atomic ensembles generated by a new developed method based on laser manipulation and{} single-photon detection.
We propose to entangle macroscopic atomic ensembles in cavity using EPR-correlated beams. We show how the field entanglement can be almost perfectly mapped onto the long-lived atomic spins associated with the ground states of the ensembles, and how it can be retrieved in the fields exiting the cavities after a variable storage time. Such a continuous variable quantum memory is of interest for manipulating entanglement in quantum networks.
We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Walls interaction range with perspectives for entangling large and distant ensembles.
We consider a scheme of multiplexed cold atomic ensembles that generate a frequency-entangled biphoton state with controllable entropy of entanglement. The biphoton state consists of a telecommunication photon (signal) immediately followed by an infrared one (idler) via four-wave mixing with two classical pump fields. Multiplexing the atomic ensembles with frequency and phase-shifted signal and idler emissions, we can manipulate and control the spectral property of the biphoton state. Mapping out the entropy of entanglement in the scheme provides the optimal configuration for entanglement reso…
Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrowband photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrowband photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-enta…
We analyze multipartite entanglement between atomic ensembles within quantum matter-light interfaces. In our proposal, a polarized light beam crosses sequentially several polarized atomic ensembles impinging on each of them at a given angle α_i. These angles are crucial parameters for shaping the entanglement since they are directly connected to the appropriate combinations of the collective atomic spins that are squeezed. We exploit such scheme to go beyond the pure state paradigm proposing realistic experimental settings to address multipartite mixed state entanglement in continuous variable…
We characterize correlations in polarization and time of photon pairs generated from a cold cloud of Rb-87 atoms via a four-wave mixing process in a cascade level scheme. Quantum state tomography reveals entangled polarization states of high purity for each of the decay paths through two different intermediate hyperfine levels. When allowing both decay paths, we observe quantum beats in time-resolved correlation measurements.
Atomic ensembles are effective memory nodes for quantum communication network due to the long coherence time and the collective enhancement effect for the nonlinear interaction between an ensemble and a photon. Here we investigate the possibility of achieving the entanglement distillation for nonlocal atomic ensembles by the input-output process of a single photon as a result of cavity quantum electrodynamics. We give an optimal entanglement concentration protocol (ECP) for two-atomic-ensemble systems in a partially entangled pure state with known parameters and an efficient ECP for the system…
We report on the storage of orbital angular momentum of light in a cold ensemble of cesium atoms. We employ Bragg diffraction to retrieve the stored optical information impressed into the atomic coherence by the incident light fields. The stored information can be manipulated by an applied magnetic field and we were able to observe collapses and revivals due to the rotation of the stored atomic Zeeman coherence for times longer than 15 $μs$.
An experimental feasible scheme is proposed to generate Greenberger-Horne-Zeilinger (GHZ) type of maximal entanglement. Distinguishing from the previous schemes, this entanglement can be chosen between either atomic ensembles (stationary qubit) or individual photons (flying qubit), according to the difference applications we desire for it. The physical requirements of the scheme are moderate and well fit the present experimental techinque.
Heralded entanglement between collective excitations in two atomic ensembles is probabilistically generated, stored, and converted to single photon fields. By way of the concurrence, quantitative characterizations are reported for the scaling behavior of entanglement with excitation probability and for the temporal dynamics of various correlations resulting in the decay of entanglement. A lower bound of the concurrence for the collective atomic state of 0.9\pm 0.3 is inferred. The decay of entanglement as a function of storage time is also observed, and related to the local dynamics.
Quantum protocols will be more efficient with high-dimensional entangled states. Photons carrying orbital angular momenta can be used to create a high-dimensional entangled state. In this paper we experimentally demonstrate the entanglement of the orbital angular momentum between the Stokes and anti-Stokes photons generated in a hot atomic ensemble using spontaneous four-wave-mixing. This experiment also suggests the existence of the entanglement concerned with spatial degrees of freedom between the hot atomic ensemble and the Stokes photon.
We present a protocol for increasing the entanglement between two atomic ensembles based on applying an approximate atom-light beamsplitter transformation to both ensembles. The effective asymmetric atom-light beamsplitter is created via a double-pass quantum non-demolition interaction between polarized light and a spin polarized atomic ensemble, derived from the linearised dipole interaction. The entanglement concentration protocol itself uses the procrustean method, similar to that first devised for light by Browne et al [2003 Phys Rev A 67 062320] and includes photon counting after the inte…
We propose a scheme for the creation of robust entanglement between a movable mirror and atomic ensemble at the macroscopic level in coupled optomechanical system. In experimentally accessible parameter regimes, we show that critical temperature of the bipartite continuous variable entanglement in our scheme can be raised from previous 24 K [Vitali {\it et al.}, Phys. Rev. Lett. \textbf{98}, 030405 (2007)] and 20 K [Genes {\it et al.}, Phys. Rev. A \textbf{77}, 050307(R) (2008)] to 32 K. We also investigate the entanglement transfer based on this coupled system. The scheme can be used for the …
We study the dynamical stability of the entanglement between the two spin ensembles in the presence of an environment. For a comparative study, we consider the two cases: a single spin ensemble, and two ensembles linearly coupled to a bath, respectively. In both circumstances, we assume the validity of the Markovian approximation for the bath. We examine the robustness of the state by means of the growth of the linear entropy which gives a measure of the purity of the system. We find out macroscopic entangled states of two spin ensembles can stably exist in a common bath. This result may be ve…
We propose a scheme of generating and verifying mesoscopic-level entanglement between two atomic ensembles using non-resonant stimulated Raman scattering. Entanglement can be generated by direct detection or balanced homodyne detection of the Stokes fields from the two cells, after they interfere on a beam splitter. The entanglement of the collective atomic fields can be transferred to the anti-Stokes fields in a readout process. By measuring the operator moments of the anti-Stokes fields, we can verify the presence of entanglement. We model the effects of practical factors such as Stokes fiel…
It is crucial for physical realization of quantum information networks to first establish entanglement among multiple space-separated quantum memories and then at a user-controlled moment to transfer the stored entanglement to quantum channels for distribution and conveyance of information. Here we present an experimental demonstration on generation, storage and transfer of deterministic quantum entanglement among three spatially separated atomic ensembles. The off-line prepared multipartite entanglement of optical modes is mapped into three distant atomic ensembles to establish entanglement o…
Hybrid matter-photon entanglement is the building block for quantum networks. It is very favorable if the entanglement can be prepared with a high probability. In this paper, we report the deterministic creation of entanglement between an atomic ensemble and a single photon by harnessing Rydberg blockade. We design a scheme that creates entanglement between a single photon's temporal modes and the Rydberg levels that host a collective excitation, using a process of cyclical retrieving and patching. The hybrid entanglement is tested via retrieving the atomic excitation as a second photon and pe…
We present a protocol for performing entanglement connection between pairs of atomic ensembles in the single excitation regime. Two pairs are prepared in an asynchronous fashion and then connected via a Bell measurement. The resulting state of the two remaining ensembles is mapped to photonic modes and a reduced density matrix is then reconstructed. Our observations confirm for the first time the creation of coherence between atomic systems that never interacted, a first step towards entanglement connection, a critical requirement for quantum networking and long distance quantum communications…
In this paper we provide an operational method to detect multipartite entanglement in ensemble-based quantum computing. This method is based on the concept of entanglement witness. We decompose the entanglement witness for each class of multipartite entanglement into nonlocal operations in addition to local measurements. Individual single qubit measurements are performed simultaneously, hence complete detection of entanglement is performed in a single run experiment. This approach is particularly important for experiments where it is operationally difficult to prepare several copies of an unkn…
The Einstein-Podolsky-Rosen (EPR) entanglement is of special importance not only for fundamental research in quantum mechanics, but also for quantum information processing. Establishing EPR entanglement between two memory systems, such as atomic ensembles, nitrogen-vacancy centers, and rare-earth-ion-doped solids is promising for realizing spatial-multimode based quantum communication, quantum computation, and quantum imaging. To date, there have been few reports on realizing EPR entanglement between physical systems in true position and momentum. Here we describe successfully establishing suc…
The entanglement of multi-atom quantum states is considered. In order to cancel noise due to inhomogeneous light atom coupling, the concept of matched multi-atom observables is proposed. As a means to eliminate an important form of decoherence this idea should be of broad relevance for quantum information processing with atomic ensembles. The general approach is illustrated on the example of rotation angle measurement, and it is shown that the multi-atom states that were thought to be only weakly entangled can exhibit near-maximum entanglement.
To establish an applicable system for advanced quantum information processing between light and atoms, we have demonstrated the quantum non-demolition (QND) measurement with a collective spin of cold ytterbium atoms (171Yb), and observed 1.8 (-1.5, +2.4) dB spin squeezing. Since a 171Yb atom has only a nuclear spin of 1/2 in the ground state, the system is the simplest spin ensemble and robust against decoherence. We used very short pulses with the width of 100 ns, so the interaction time became much shorter than the decoherence time, which is important for multi-step quantum information proce…
We theoretically investigate the spectral entanglement of a multiphoton source generated from the cascade emissions in the cascaded cold atomic ensembles.\ This photon source is highly directional, guaranteed under the four-wave mixing condition, and is also highly frequency-correlated due to finite driving pulse durations and superradiant decay constants.\ We utilize Schmidt decomposition to study the bipartite entanglement of the biphoton states projected from the multiphoton ones.\ This entropy of entanglement can be manipulated by controlling the driving parameters and superradiant decay r…
We describe an experimental scheme of preparing multipartite W class of maximally entangled states between many atomic ensembles. The scheme is based on laser manipulation of atomic ensembles and single-photon detection, and well fits the status of the current experimental technology. In addition, we show one of the applications of the kind of W class states, teleporting an entangled state of atomic ensembles with unknown coefficients to more than one distant parties, either one of which equally likely receives the transmitted state.
Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimenta…
We describe a general technique that allows for an ideal transfer of quantum correlations between light fields and metastable states of matter. The technique is based on trapping quantum states of photons in coherently driven atomic media, in which the group velocity is adiabatically reduced to zero. We discuss possible applications such as quantum state memories, generation of squeezed atomic states, preparation of entangled atomic ensembles and quantum information processing.
Bernstein and Varizani have given the first quantum algorithm to solve parity problem in which a strong violation of the classical imformation theoritic bound comes about. In this paper, we refine this algorithm with fewer resource and implement a two qubits algorithm in a single query on an ensemble quantum computer for the first time.
We investigate how entangled coherent states and superpositions of low intensity coherent states of non-Gaussian nature can be generated via non-resonant interaction between either two linearly or circularly polarized field modes and an ensemble of X-like four-level atoms placed in an optical cavity. We compare our results to recent experimental observations and argue that the non-Gaussian structure of the field states may be present in those systems.
We characterize a source of photon pairs based on cascade decay in a cold Rb-87 ensemble. This source is particularly suited to generate of photons for interaction with Rb-87 based atomic systems. We experimentally investigate the dependence of pair generation rate, single photon heralding efficiency, and bandwidth as a function of the number of atoms, detuning and intensity of the pump beams. The observed power and detuning behaviors can be explained by the steady state solution of an established three-level model of an atom. Measurements presented here provide a useful insight on the optimiz…
Multiparticle entangled states generated via interaction between narrow-band light and an ensemble of identical two-level atoms are considered. Depending on the initial photon statistics, correlation between atoms and photons can give rise to entangled states of these systems. It is found that the state of any pair of atoms interacting with weak single-mode squeezed light is inseparable and robust against decay. Optical schemes for preparing entangled states of atomic ensembles by projective measurement are described.
Entangled quantum states in high-dimensional space show many advantages compared with entangled states in two-dimensional space. The former enable quantum communication with higher channel capacity, enable more efficient quantum-information processing, and are more feasible for closing the detection loophole in Bell test experiments. Establishing high-dimensional entangled memories is essential for long-distance communication, but its experimental realization is lacking. We experimentally established high-dimensional entanglement in orbital angular momentum space between two atomic ensembles s…
Analysis of the spontaneously induced correlation on atom-radiation entanglement in an ensemble of two-level atoms initially prepared in the upper level and placed in a cavity containing a squeezed radiation employing the method of evaluating the coherent-state propagator is presented. It is found that the cavity radiation exhibits squeezing which is directly attributed to the squeezed radiation in the cavity. The intensity of the cavity radiation increases with the squeeze parameter and interaction time. It is also shown that substantial degree of entanglement between the atomic states and ra…
We report the generation of a macroscopic singlet state in a cold atomic sample via quantum non-demolition (QND) measurement induced spin squeezing. We observe 3 dB of spin squeezing and detect entanglement of up to $5.5\times10^5 $ atoms with $5σ$ statistical significance using a generalized spin squeezing inequality. The degree of squeezing implies at least 50% of the atoms have formed singlets, while the response to a magnetic field gradient indicates entanglement bonds at all length scales, a characteristic of quantum spin liquids.
Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into ensemble of pure states of Schmidt rank 1 or 2. That is, the Schmidt number of the density matrix must be equal to or greater than 3.
We present two protocols, one for the storage of light in an atomic ensemble and the subsequent retrieval, and another one for the generation of entanglement between light and atoms. They rely on two passes of a single pulse through the ensemble, Larmor precessing in an external field. Both protocols work deterministically and the relevant figures of merit - such as the fidelity or the EPR variance - scale exponentially in the coupling strength. We solve the corresponding Maxwell-Bloch equations describing the scattering process and determine the resulting input-output relations which only inv…
We propose a method that enables efficient frequency conversion of quantum information based on recently demonstrated strong parametric coupling between two single-photon pulses propagating in a slow-light atomic medium at different group velocities. We show that an incoming single-photon state is efficiently converted into another optical mode in a lossless and shape-conserving manner. The persistence of initial quantum coherence and entanglement within frequency conversion is also demonstrated. We first illustrate this result for the case of small frequency difference of converted photons, a…
Here we present an experimentally feasible scheme to entangle flying qubit (individual photon with polarization modes) and stationary qubit (atomic ensembles with long-lived collective excitations). This entanglement integrate two different species can act as a critical element for the coherent transform of quantum information between flying and stationary qubits. The entanglement degree can be also adjusted expediently with linear optics. Furthermore, the present scheme can be modified to generate this entanglement in a way event-ready with the employment of a pair of entangled photons. Then …
Recent results, extending the Schmidt decomposition theorem to wavefunctions of identical particles, are reviewed. They are used to give a definition of reduced density operators in the case of two identical particles. Next, a method is discussed to calculate time averaged entanglement. It is applied to a pair of identical electrons in an otherwise empty band of the Hubbard model, and to a pair of bosons in the the Bose-Hubbard model with infinite range hopping. The effect of degeneracy of the spectrum of the Hamiltonian on the average entanglement is emphasised.
We show how to construct a multi-qubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other N-1 qubits. We provide an algorithm how to build up an array of networks consisting of single-qubit rotations and multi-qubit control-NOT gates for the synthesis of an arbitrary entangled quantum state of N qubits. We illustrate the algorithm on a system of cold trapped ions. This example illuminates the efficiency of the direct implementation of the multi-qubit CNOT gate compared to its decomposition…
We present a simplified version of a repeater protocol in a cold neutral-atom ensemble with Rydberg excitations optimized for two-node entanglement generation and describe a protocol for quantum teleportation. Our proposal draws from previous proposals [Zhao, {\sl et al.}, Phys. Rev. A {\bf 81}, 052329 (2010)] and [Han, {\sl et al.} Phys. Rev. A {\bf 81}, 052311 (2010)] who described efficient and robust protocols for long-distance entanglement with many nodes. Using realistic experimental values we predict an entanglement generation rate of $\sim$25 Hz and teleportation rate of $\sim$ 5 Hz. O…
The Einstein Podolsky Rosen (EPR) entangled quantum state is of special importance not only for fundamental research in quantum mechanics, but also for information processing in the field of quantum information. Previous EPR entangled state demonstrations were constructed with photons of equal phase wave fronts. More complex scenarios with structured wave fronts have not been investigated. Here, we report the first experimental demonstration of EPR entanglement for photon pairs carrying orbital angular momentum (OAM) information, resulting in an OAM embedded EPR entangled state. We measured th…
We present a scheme to implement a steady lightwave-photon-and-magnon entanglement in a hybrid photon-magnon system by adiabatically eliminating the auxiliary microwave cavity and effectively laser cooling a delocalized Bogoliubov mode. The system consists of magnons, lightwave and microwave photons, and phonons. The magnons are embodied by a collective motion of a large number of spins in a macroscopic ferrimagnet. To achieve an entangling interaction between magnons and lightwave photons, we drive optical cavity and magnon at the red and blue sideband associated with the mechanical resonator…
