Atomic Entangled States Research Articles

Memoryless Quantum Repeaters Based on Cavity‐QED and Coherent States

AbstractA quantum repeater scheme based on cavity‐quantum electrodynamics (QED) and quantum error correction of channel loss via rotation‐symmetric bosonic codes (RSBCs) is proposed to distribute atomic entangled states over long distances without memories and at high clock rates. In this scheme, controlled rotation gates, i.e., phase shifts of the propagating light modes conditioned upon the state of an atom placed in a cavity, provide a mechanism both for the entangled‐state preparations and for the error syndrome identifications. In order to assess the performance of this repeater protocol, an explicit instance of RSBCs—multicomponent cat codes—are studied quantitatively. It is found that the total fidelity and the success probability for quantum communication over a long distance (such as 1000 km) both can almost approach unity provided a small enough elementary distance between stations (smaller than 0.1 or 0.01 km) and rather low local losses (up to 0.1%) are considered. In a quantum key distribution application, secret key rates can become correspondingly high, both per channel use, beating the repeaterless bound, and per second thanks to the relatively high clock rates of the memoryless scheme. Based upon the cavity‐QED setting, this scheme can be realized at room temperature and at optical frequencies.

Tunable Directional Emission and Collective Dissipation with Quantum Metasurfaces

Subwavelength atomic arrays, recently labeled as quantum metamaterials, have emerged as an exciting platform for obtaining novel quantum optical phenomena. The strong interference effects in these systems generate subradiant excitations that propagate through the atomic array with very long lifetimes. Here, we demonstrate that one can harness these excitations to obtain tunable directional emission patterns and collective dissipative couplings when placing judiciously additional atoms nearby the atomic array. For doing that, we first characterize the optimal square array geometry to obtain directional emission patterns. Then, we characterize the best atomic positions to couple efficiently to the subradiant metasurface excitations and provide several improvement strategies based on entangled atomic clusters or bilayers. Afterward, we also show how the directionality of the emission pattern can be controlled through the relative dipole orientation between the auxiliary atoms and the one of the array. Finally, we benchmark how these directional emission patterns translate into to collective, anisotropic dissipative couplings between the auxiliary atoms by studying the lifetime modification of atomic entangled states.

Distributed Entangled State Production by Using Quantum Repeater Protocol

We consider entangled state production utilizing a full optomechanical arrangement, based on which we create entanglement between two far three-level V-type atoms using a quantum repeater protocol. At first, we consider eight identical atoms (1; 2;...; 8), while adjacent pairs (i; i + 1) with i = 1; 3; 5; 7 have been prepared in entangled states and the atoms 1, 8 are the two target atoms. The three-level atoms (1,2,3,4) and (5,6,7,8) distinctly become entangled with the system including optical and mechanical modes by performing the interaction in optomechanical cavities between atoms (2,3) and (6,7), respectively. Then, by operating appropriate measurements, instead of Bell state measurement which is a hard task in practical works, the entangled states of atoms (1,4) and (5,8) are achieved. Next, via interacting atoms (4,5) of the pairs (1,4) and (5,8) and operating proper measurement, the entangled state of target atoms (1,8) is obtained. In the continuation, entropy and success probability of the produced entangled state are then evaluated. It is observed that the time period of entropy is increased by increasing the mechanical frequency and by decreasing optomechanical coupling strength to the field modes. Also, in most cases, the maximum of success probability is increased by decreasing G and via decreasing.

Atom–atom entanglement via coherent photons in a nonlinear optical cavity

In the present article, dynamics of entanglement between two different two-level atoms, as nonidentical qubits, via monochromatic coherent photons is explored. The atoms are embedded in an optical lossless cavity filled with a centrosymmetric dielectric. A conserved (Casimir) operator, i.e. a dynamic integral of motion, is introduced to decompose the matrix representation of the total atom–photon Hamiltonian into direct sum of irreducible blocks. Using the eigenvalues and eigenvectors of the blocks, the time evolution unitary operator of the system is computed. The time-dependent atomic density operator is then calculated by partial tracing of atom–field density operator over photonic states for both initially separable and maximally entangled atomic states. The partially transposed atomic density operator, with respect to one of the atomic subsystems, is finally used to determine the negativity as an entanglement quantifier. Our results indicate that the robust entanglement is observed when the initial maximally atomic entangled state is applied. Furthermore, as Kerr-type coupling (arising from the third-order susceptibility of the centrosymmetric dielectric) increases it is shown that the entanglement enhances. In addition, effects of the initial atomic state preparation, the atom–photon structure parameters as well as field intensity on the entanglement birth and death are also addressed.

Characterization of Errors in Interferometry with Entangled Atoms

Recent progress in generating entangled spin states of neutral atoms provides opportunities to advance quantum sensing technology. In particular, entanglement can enhance the performance of accelerometers and gravimeters based on light-pulse atom interferometry. We study the effects of error sources that may limit the sensitivity of such devices, including errors in the preparation of the initial entangled state, imperfections in the laser pulses, momentum spread of the initial atomic wave packet, measurement errors, spontaneous emission, and atom loss. We determine that, for each of these errors, the expectation value of the parity operator $\Pi$ has the general form, $\overline{\langle \Pi \rangle} = \Pi_0 \cos( N \phi )$, where $\phi$ is the interferometer phase and $N$ is the number of atoms prepared in the maximally entangled Greenberger--Horne--Zeilinger state. Correspondingly, the minimum phase uncertainty has the general form, $\Delta\phi = (\Pi_0 N)^{-1}$. Each error manifests itself through a reduction of the amplitude of the parity oscillations, $\Pi_0$, below the ideal value of $\Pi_0 = 1$. For each of the errors, we derive an analytic result that expresses the dependence of $\Pi_0$ on error parameter(s) and $N$, and also obtain a simplified approximate expression valid when the error is small. Based on the performed analysis, entanglement-enhanced atom interferometry appears to be feasible with existing experimental capabilities.

Thermal entanglement and teleportation via thermally atomic entangled state in cavity QED

In this article, we study thermal entanglement between two-coupled two-level atoms interacting with a single-mode cavity field. The cavity mode is assumed to be initially in the vacuum state and the detuning parameter is large. The thermal entanglement in this two-qubit system is quantified in terms of the concurrence, as a proper measure for two-qubit mixed states. We investigate how the thermal entanglement depends on temperature, dipole coupling between the atoms and detuning parameter. In addition, we shall use the generated thermally atomic entangled state as a quantum channel for teleportation and we mainly concentrate on the fidelity of teleportation. Finally, the relationship between the quantum coherence and entanglement will be discussed.

Quantum metrology enhanced by coherence-induced driving in a cavity-QED setup

We propose a quantum metrology scheme in a cavity QED setup to achieve the Heisenberg limit. In our scheme, a series of identical two-level atoms randomly pass through and interact with a dissipative single-mode cavity. Different from the entanglement based Heisenberg limit metrology scheme, we do not need to prepare the atomic entangled states before they enter into the cavity. We show that the initial atomic coherence will induce an effective driving to the cavity field, whose steady state is an incoherent superposition of orthogonal states, with the superposition probabilities being dependent on the atom-cavity coupling strength. By measuring the average photon number of the cavity in the steady state, we demonstrate that the root-mean-square of the fluctuation of the atom-cavity coupling strength is proportional to $1/N_c^2$ ($N_c$ is the effective atom number interacting with the photon in the cavity during its lifetime). It implies that we have achieved the Heisenberg limit in our quantum metrology process. We also discuss the experimental feasibility of our theoretical proposal. Our findings may find potential applications in quantum metrology technology.

Generation of various classes of entangled states in a two-mode Bose–Einstein condensate under the influence of interatom collisions

In this paper, we generate some new classes of entangled states of a bimodal Bose–Einstein condensate (BEC), a pair of tunnel-coupled BEC, in the presence of two- and three-body elastic as well as mode-exchange collisions. The Hamiltonian of the considered system is very complicated, moreover, it can be fortunately transformed into a simple form using a two-mode displacement operator. After introducing the general form of the time evolved state, various classes of entangled states are generated. Indeed, the influence of different orders of tunneling strengths on the generated entangled states has been studied. Depending on the tunneling strength constants, two-, three- and four-partite entangled states are generated, all of which are superposition states of macroscopic number of BEC atoms. Considering three-particle collision dramatically changes the generated entangled states. Moreover, in particular cases, the resulted states are non-entangled. Also, we show that tunneling and collisional interactions can be manipulated to generate a pair of atomic entangled coherent states (quasi-Bell states). In addition, it is observed that the degree of entanglement for two-partite entangled states can be tuned via the number of BEC atoms, i.e. the corresponding concurrences tend to their maximum value by increasing the atoms in both modes of system.

Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup

We propose a dissipative scheme to prepare maximally entangled steady states in cavity QED setup, consisting of two two-level atoms interacting with the two counter-propagating whispering-gallery modes (WGMs) of a microtoroidal resonator. Using spontaneous emission and cavity decay as the dissipative quantum dynamical source, we show that the steady state of this system can be steered into a two-atom single state as well as into a two-mode single state. We probed the compound system with weak field coupled to the system via a tapered fiber waveguide, finding it is possible to determine whether the two atoms or two modes are driven to a maximally entangled state. Through the transmission and reflection measurements, without disturbing the atomic state, when the cavity modes are being driven, or without disturbing the cavity field state, when a single atom being driven, one can get the information about the maximal entanglement. We also investigated for both subsystem, two-atom and two-mode states, the entanglement generation and under what conditions one can transfer entanglement from one subsystem to the other. Our scheme can be selectively used to prepare both maximally entangled atomic state as well as maximally entangled cavity-modes state, providing an efficient method for quantum information processing.

Quantum repeater using three-level atomic states in the presence of dissipation: stability of entanglement

In this paper we want to investigate the possibility of transferring entanglement to two three-level separable atomic states over long distance using the quantum repeater protocol. In detail, our model consists of eight Λ-type three-level atoms where only the pairs (1, 2), (3, 4), (5, 6) and (7, 8) are prepared in maximally entangled states. Performing suitable interaction between non-entangled three-level atoms (2, 3) and (6, 7) in two-mode cavities with photon leakage rates in the presence of spontaneous emission leads to producing entanglement between atoms (1, 4) and (5, 8), separately. Finally, the entanglement between atoms (1, 8) is successfully produced by performing interaction between atoms (4, 5) while spontaneous emission is considered in a dissipative cavity. In the continuation, the effects of detuning, dissipation sources and initial interaction time are evaluated on the negativity and success probability of the processes. It is shown that, the maxima of negativity are decreased by increasing the detuning, in most cases. Also, the time evolution of negativity is non-periodic in the presence of dissipation. In addition, increasing the initial interaction time has a constructive effect on the negativity in all considered cases. The oscillations of negativity are destroyed as time goes on and the produced entanglement becomes stable. The success probability of entangled state of atoms (1, 8) is tunable by controlling the detuning and dissipation. We show that via justifying the involved parameters one can arrive at conditions in which the decoherence effects are fully disappeared; as a result, an ideal quantum repeater can be properly achieved while atomic and field dissipations are taken into account.

Hybrid quantum repeater for qudits

We present a "hybrid quantum repeater" protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable $d$-level systems, each of, in principle, arbitrary dimension $d$, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially (but not restricted to) efficient continuous-variable homodyne detections ("hybrid" here refers to the simultaneous exploitation of discrete and continuous variable degrees of freedom for the local processing and storage of entangled states as well as their non-local distribution, respectively). For qutrits we quantify the light-matter entanglement that can be effectively shared through an elementary lossy channel, and for a repeater spacing of up to 10 km we show that the realistic (lossy) qutrit entanglement is even larger than any ideal (loss-free) qubit entanglement. After including qudit entanglement purification and swapping procedures, we calculate the long-distance entangled-pair distribution rates and the final entangled-state fidelities for total communication distances of up to 1280 km. With three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at rates of the order of, in principle, 100 Hz.

Critical slowing down of multiatom entanglement by Rydberg blockade

Laser excitation pulses that lead to perfect adiabatic state transfer in an ensemble of three-level ladder atoms lead to highly entangled states of many atoms if their highest excited state is subject to Rydberg blockade. Solution of the Schr\"odinger equation shows that it is increasingly difficult to ensure the adiabatic evolution as the number of atoms increases. A diminishing energy gap, significant variations in collective observables, and increased work fluctuations link the critical slowing down of the adiabatic evolution with a quantum phase transition-like behavior of the system.

Efficient Multiphoton Generation in Waveguide Quantum Electrodynamics.

Engineering quantum states of light is at the basis of many quantum technologies such as quantum cryptography, teleportation, or metrology among others. Though, single photons can be generated in many scenarios, the efficient and reliable generation of complex single-mode multiphoton states is still a long-standing goal in the field, as current methods either suffer from low fidelities or small probabilities. Here we discuss several protocols which harness the strong and long-range atomic interactions induced by waveguide QED to efficiently load excitations in a collection of atoms, which can then be triggered to produce the desired multiphoton state. In order to boost the success probability and fidelity of each excitation process, atoms are used to both generate the excitations in the rest, as well as to herald the successful generation. Furthermore, to overcome the exponential scaling of the probability of success with the number of excitations, we design a protocol to merge excitations that are present in different internal atomic levels with a polynomial scaling.

Heralded multiphoton states with coherent spin interactions in waveguide QED

Waveguide QED offers the possibility of generating strong coherent atomic interactions either through appropriate atomic configurations in the dissipative regime or in the bandgap regime. In this work, we show how to harness these interactions in order to herald the generation of highly entangled atomic states, which afterwards can be mapped to generate single mode multi-photonic states with high fidelities. We introduce two protocols for the preparation of the atomic states, we discuss their performance and compare them to previous proposals. In particular, we show that one of them reaches high probability of success for systems with many atoms but low Purcell factors.

Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements

Entanglement plays an important role in quantum information science, especially in quantum communications. Here we present an efficient entanglement concentration protocol (ECP) for nonlocal atom systems in the partially entangled W-class states, using the single-photon input-output process regarding low-$Q$ cavity and linear optical elements. Compared with previously published ECPs for the concentration of non-maximally entangled atomic states, our protocol is much simpler and more efficient as it employs the Faraday rotation in cavity quantum electrodynamics (QED) and the parameter-splitting method. The Faraday rotation requires the cavity with low-$Q$ factor and weak coupling to the atom, which makes the requirement for entanglement concentration much less stringent than the previous methods, and achievable with current cavity QED techniques. The parameter-splitting method resorts to linear-optical elements only. This ECP has high efficiency and fidelity in realistic experiments, and some imperfections during the experiment can be avoided efficiently with currently available techniques.

Scalable Dissipative Preparation of Many-Body Entanglement

We present a technique for the dissipative preparation of highly entangled multiparticle states of atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings, we engineer many-body dissipation that drives the system from an arbitrary initial state into a Greenberger-Horne-Zeilinger state. We demonstrate that using our technique highly entangled steady states can be prepared efficiently in a time that scales polynomially with the system size. Our protocol assumes generic couplings and will thus enable the dissipative production of multiparticle entanglement in a wide range of physical systems. As an example, we demonstrate the feasibility of our scheme in state-of-the-art trapped-ion systems.

Deterministically Entangling Two Remote Atomic Ensembles via Light-Atom Mixed Entanglement Swapping.

Entanglement of two distant macroscopic objects is a key element for implementing large-scale quantum networks consisting of quantum channels and quantum nodes. Entanglement swapping can entangle two spatially separated quantum systems without direct interaction. Here we propose a scheme of deterministically entangling two remote atomic ensembles via continuous-variable entanglement swapping between two independent quantum systems involving light and atoms. Each of two stationary atomic ensembles placed at two remote nodes in a quantum network is prepared to a mixed entangled state of light and atoms respectively. Then, the entanglement swapping is unconditionally implemented between the two prepared quantum systems by means of the balanced homodyne detection of light and the feedback of the measured results. Finally, the established entanglement between two macroscopic atomic ensembles is verified by the inseparability criterion of correlation variances between two anti-Stokes optical beams respectively coming from the two atomic ensembles.

Creation of N-atom GHZ state in atom-cavity-fiber system by multi-state adiabatic passage

We propose a relatively robust scheme to generate controllable (deterministic) atomic entangled GHZ states in atom-cavity-fiber system by adiabatic passage. In the present scheme, the atoms are individually trapped in N spatially separated optical cavities coupled by optical fibers. Losses due to the cavity decay are efficiently suppressed by employing the adiabatic passage technique and appropriately designed atom-field couplings. We consider N five-level atoms simultaneously interacting with N resonant one-mode cavity to reach the N-atom GHZ state of the present system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is also investigated. It is found that our schemes can be realized with high fidelity even when these decoherence processes are considered.

Preparation and transmission of diversified multi-particle entanglements with spatially separate cavities

We explore a feasible scheme for generating entangled states for three-level multi-atom trapped within spatially separated cavities. The scheme involves interaction-detection cycle and utilizes resonant atoms with an extra ground state not coupled to the cavity field. Additionally, the scheme can also be generalized to transmit an unknown two-atom entangled state assisted with two auxiliary atoms. Very different from the previous standard schemes, the teleportation of an unknown two atomic entangled state in our scheme is independent of the Bell-state measurement. The current scheme makes use of resonant atom-field interaction instead of Raman coupling, and thus the interaction time is greatly shortened. Furthermore, since the cavities are left in the vacuum state and the atoms are in the ground state, the prepared entanglement states are insensitive to the cavity decay and the atomic spontaneous emission.

Generation and detection of a sub-Poissonian atom number distribution in a one-dimensional optical lattice.

We demonstrate preparation and detection of an atom number distribution in a one-dimensional atomic lattice with the variance -14 dB below the Poissonian noise level. A mesoscopic ensemble containing a few thousand atoms is trapped in the evanescent field of a nanofiber. The atom number is measured through dual-color homodyne interferometry with a pW-power shot noise limited probe. Strong coupling of the evanescent probe guided by the nanofiber allows for a real-time measurement with a precision of ±8 atoms on an ensemble of some 10(3) atoms in a one-dimensional trap. The method is very well suited for generating collective atomic entangled or spin-squeezed states via a quantum nondemolition measurement as well as for tomography of exotic atomic states in a one-dimensional lattice.