I consider several interesting aspects of a new light source, a two-level atom, or N two-level atoms inside an Optical Parametric Oscillator. We find that in the weak driving limit, detection of a transmitted or fluorescent photon generates a highly entangled state of the atom and the cavity. This entanglement can be used with beamsplitters to create more complex quantum states and implement teleportation protocols. Also, one can store a single photon in the atoms, along the lines of recent slow and stopped light proposals and experiments.
We analyse the fidelity of teleportation protocols, as a function of resource entanglement, for three kinds of two mode oscillator states: states with fixed total photon number, number states entangled at a beam splitter, and the two-mode squeezed vacuum state. We define corresponding teleportation protocols for each case including phase noise to model degraded entanglement of each resource.
We provide a quantum benchmark for teleportation and storage of single-mode squeezed states with zero displacement and a completely unknown degree of squeezing along a given direction. For pure squeezed input states, a fidelity higher than 81.5% has to be attained in order to outperform any classical strategy based on an estimation of the unknown squeezing and repreparation of squeezed states. For squeezed thermal input states, we derive an upper and a lower bound on the classical average fidelity which tighten for moderate degree of mixedness. These results enable a critical discussion of rec…
In this paper we present an optimal protocol by which an unknown state on a Hilbert space of dimension $N$ can be approximately stored in an $M$-dimensional quantum system or be approximately teleported via an $M$-dimensional quantum channel. The fidelity of our procedure is determined for pure states as well as for mixed states and states which are entangled with auxiliary quantum systems of varying Hilbert space dimension, and it is compared with theoretical results for the maximally achievable fidelity.
We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing $s$ is fixed, no information about its orientation in phase space is given, and the distribution of phase space displacements is a Gaussian. In the limit where the latter becomes flat, we prove analytically that the maximal classical achievable fidelity (which is 1/2 without squeezing, for $s=1$) is given by $\sqrt{s}/(1+s)$, vanishing when the degree of squeezing diverges. For mixed states, as well as for general distribut…
A quantum communication system is proposed that uses polarization-entangled photons and trapped-atom quantum memories. This system is capable of long-distance, high-fidelity teleportation, and long-duration quantum storage.
A one-dimensional topological superconductor features a single fermionic zero mode that is delocalized over two Majorana bound states located at the ends of the system. We study a pair of spatially separated nanomechanical oscillators tunnel-coupled to these Majorana modes. Most interestingly, we demonstrate that the combination of electron-phonon coupling and a finite charging energy on the mesoscopic topological superconductor can lead to an effective superexchange between the oscillators via the non-local fermionic zero mode. We further show that this teleportation mechanism leads to entang…
We describe two protocols for efficient data transmission using a single passive bus. Different types of interactions are obtained enabling deterministic transfer and teleportation of composite quantum systems for arbitrary subsystem dimension and for arbitrary numbers of subsystems. The subsystems may become entangled in the transmission in which case the protocols can serve generalized teleportation based information processing as well as storage and transmission functions. We explore the cases of two qubits and two qutrits in detail, obtaining a maximally entangling mapping of the composite…
A protocol of quantum energy teleportation is proposed for a one-dimensional harmonic chain. A coherent-state POVM measurement is performed to coupled oscillators of the chain in the ground state accompanied by energy infusion to the system. This measurement consumes a part of ground state entanglement. Depending on the measurement result, a displacement operation is performed on a distant oscillator accompanied by energy extraction from the zero-point fluctuation of the oscillator. We find that the amount of consumed entanglement is bounded from below by a positive value that is proportional …
We propose an experimental protocol to realize discrete variable quantum teleportation using optomechanical devices. The photonic polarization superposition state of a single photon is teleported to a phononic superposition of two micromechanical oscillators by means of photon/phonon entanglement generation and optical Bell state measurement using two-photon interference. Verification of the protocol is performed by coherent state transfer between the mechanical devices and light. Simulations show the feasibility of the proposed scheme at millikelvin temperatures using state-of-the-art gigaher…
Recently, we have shown theoretically [1] as well as experimentally [2] how the phase of an electromagnetic field can be determined by measuring the population of either of the two states of a two-level atomic system excited by this field, via the so-called Bloch-Siegert oscillation resulting from the interference between the co- and counter-rotating excitations. Here, we show how a degenerate entanglement, created without transmitting any timing signal, can be used to teleport this phase information. This phase-teleportation process may be applied to achieve wavelength teleportation, which in…
Light is an irreplaceable means of communication among various quantum information processing and storage devices. Due to their different physical nature, some of these devices couple more strongly to discrete, and some to continuous degrees of freedom of a quantum optical wave. It is therefore desirable to develop a technological capability to interconvert quantum information encoded in these degrees of freedom. Here we generate and characterize an entangled state between a dual-rail (polarization-encoded) single-photon qubit and a qubit encoded as a superposition of opposite-amplitude cohere…
Schrödinger's thought experiment to prepare a cat in a superposition of both alive and dead states reveals profound consequences of quantum mechanics and has attracted enormous interests. Here we propose a straightforward method to create quantum superposition states of a living microorganism by putting a small cryopreserved bacterium on top of an electromechanical oscillator. Our proposal is based on recent developments that the center-of-mass oscillation of a 15-$μ$m-diameter aluminium membrane has been cooled to its quantum ground state [Nature 475: 359 (2011)], and entangled with a microwa…
Future quantum internet applications will derive their power from the ability to share quantum information across the network. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections. While many experimental demonstrations have been performed on different quantum network platforms, moving beyond directly connected nodes has so far been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation bet…
We generalize the experimental success criterion for quantum teleportation/memory in continuous-variable quantum systems to be suitable for non-unit-gain condition by considering attenuation/amplification of the coherent-state amplitude. The new criterion can be used for a non-ideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in quantum domain.
We consider the storage and transmission of a Gaussian distributed set of coherent states of continuous variable systems. We prove a limit on the average fidelity achievable when the states are transmitted or stored by a classical channel, i.e., a measure and repreparation scheme which sends or stores classical information only. The obtained bound is tight and serves as a benchmark which has to be surpassed by quantum channels in order to outperform any classical strategy. The success in experimental demonstrations of quantum memories as well as quantum teleportation has to be judged on this f…
Using the quantum teleportation in continuous variables as a test scheme, we compare two entangled transformations - mixing of signals on a beamsplitter and by the CZ operation. We evaluate these transformations in terms of the errors added to teleported oscillators. We have shown that the CZ operation leads to the lower error of teleportation. This error can be further reduced by choosing appropriate weight coefficients for the CZ transforms. We have compared the errors of the theoretical CZ scheme and its practical implementation in the optical design. Although the CZ optical scheme adds int…
Nonperturbative analysis of quantum entanglement and quantum teleportation protocol using oscillator variables carried by observers in relativistic motion under the continuous influence of the environment is given. The full time evolution of quantum entanglement among static and accelerated observers is studied. The environment plays a dual role. While it creates bipartite and tripartite entanglement among observers even when the initial state is separable, it suppresses the entanglement via decoherence. Motivated by the black hole information problem, we consider quantum teleportation between…
Transfer of quantum information between physical systems of a different nature is a central matter in quantum technologies. Particularly challenging is the transfer between discrete- and continuous degrees of freedom of various harmonic oscillator systems. Here we implement a protocol for teleporting a continuous-variable optical qubit, encoded by means of coherent states, onto a discrete-variable, single-rail qubit - a superposition of the vacuum- and single-photon optical states - via a hybrid entangled resource. We test our protocol on coherent states of different phases and obtain the tele…
We report a 65MHz-bandwidth triangular-shaped optical parametric oscillator (OPO) for squeezed vacuum generation at 860nm. The triangle structure of our OPO enables the round-trip length to reach 45mm as a ring cavity, which provides a counter circulating optical path available for introducing a probe beam or generating another squeezed vacuum. Hence our OPO is suitable for the applications in high-speed quantum information processing where two or more squeezed vacua form a complicated interferometer, like continuous-variable quantum teleportation. With a homemade, broadband and low-loss homod…
Entangling a mechanical oscillator with an optical mode is an enticing and yet a very challenging goal in cavity optomechanics. Here we consider a pulsed scheme to create Einstein-Podolsky-Rosen-type entanglement between a traveling-wave light pulse and a mechanical oscillator. The entanglement can be verified unambiguously by a pump-probe sequence of pulses. In contrast to schemes that work in a steady-state regime under a continuous-wave drive, this protocol is not subject to stability requirements that normally limit the strength of achievable entanglement. We investigate the protocol's per…
We investigate a family of qubit-oscillator states as resources for hybrid quantum communication. They result from a mechanism of qubit-controlled displacement on the oscillator. For large displacements, we obtain analytical formulas for entanglement and other nonclassical correlations, such as entropic and geometric discord, in those states. We design two protocols for quantum communication using the considered resource states, a hybrid teleportation and a hybrid remote state preparation. The latter, in its standard formulation, is shown to have a performance limited by the initial mixedness …
A promising route to novel quantum technologies are hybrid quantum systems, which combine the advantages of several individual quantum systems. We have realized a hybrid atomic-mechanical experiment consisting of a SiN membrane oscillator cryogenically precooled to 500 mK and optically coupled to a cloud of laser cooled Rb atoms. Here, we demonstrate active feedback cooling of the oscillator to a minimum mode occupation of n = 16 corresponding to a mode temperature of T = 200 μK. Furthermore, we characterize in detail the coupling of the membrane to the atoms by means of sympathetic cooling. B…
Considering a network of dissipative quantum harmonic oscillators we deduce and analyze the optimum topologies which are able to store, for the largest period of time, a quantum superposition previously prepared in one of the network oscillators. The storage of the superposition is made dynamically, in that the state to be protected evolves through the network before being retrieved back in the oscillator where it was prepared. The decoherence time during the dynamic storage process is computed and we demonstrate that it is proportional to the number of oscillators in the network for a particu…
Quantum teleportation and quantum memory are two crucial elements for large-scale quantum networks. With the help of prior distributed entanglement as a "quantum channel", quantum teleportation provides an intriguing means to faithfully transfer quantum states among distant locations without actual transmission of the physical carriers. Quantum memory enables controlled storage and retrieval of fast-flying photonic quantum bits with stationary matter systems, which is essential to achieve the scalability required for large-scale quantum networks. Combining these two capabilities, here we reali…
The realization of a quantum interface between a propagating photon used for transmission of quantum information, and a stationary qubit used for storage and manipulation, has long been an outstanding goal in quantum information science. A method for implementing such an interface between dissimilar qubits is quantum teleportation, which has attracted considerable interest not only as a versatile quantum-state-transfer method but also as a quantum computational primitive. Here, we experimentally demonstrate transfer of quantum information carried by a photonic qubit to a quantum dot spin qubit…
We propose an efficient method for mapping and storage of a quantum state of propagating light in atoms. The quantum state of the light pulse is stored in two sublevels of the ground state of a macroscopic atomic ensemble by activating a synchronized Raman coupling between the light and atoms. We discuss applications of the proposal in quantum information processing and in atomic clocks operating beyond quantum limits of accuracy. The possibility of transferring the atomic state back on light via teleportation is also discussed.
Storage and distribution of quantum information are key elements of quantum information processing and quantum communication. Here, using atom-photon entanglement as the main physical resource, we experimentally demonstrate the preparation of a distant atomic quantum memory. Applying a quantum teleportation protocol on a locally prepared state of a photonic qubit, we realized this so-called remote state preparation on a single, optically trapped 87Rb atom. We evaluated the performance of this scheme by the full tomography of the prepared atomic state, reaching an average fidelity of 82%.
We investigate quantum teleportation of ensembles of coherent states of light with a Gaussian distributed displacement in phase space. Recently, the following general question has been addressed in [P. Liuzzo-Scorpo et al., arXiv:1705.03017]: Given a limited amount of entanglement and mean energy available as resources, what is the maximal fidelity that can be achieved on average in the teleportation of such an alphabet of states? Here, we consider a variation of this question, where Einstein-Podolsky-Rosen steering is used as a resource rather than plain entanglement. We provide a solution by…
We give a quantum benchmark for teleportation and quantum storage experiments suited for pure and mixed test states. The benchmark is based on the average fidelity over a family of phase-covariant states and certifies that an experiment can not be emulated by a classical setup, i.e., by a measure-and-prepare scheme. We give an analytical solution for qubits, which shows important differences with standard state estimation approach, and compute the value of the benchmark for coherent and squeezed states, both pure and mixed.
We analyze a method for the creation, storage and retrieval of optomechanical Schrodinger cat states, in which there is a quantum superposition of two distinct macroscopic states of a mechanical oscillator. In the proposal, an optical cat state is first prepared in an optical cavity, then transferred to the mechanical mode, where it is stored and later retrieved using control fields. We carry out numerical simulations for the quantum memory protocol for optomechanical cat states using the positive-P phase space representation. This has a compact, positive representation for a cat state, thus a…
Dark-Mode Control of Contrasting Entanglement and Bell Nonlocality between Mechanical Oscillators
IMEC；Hasselt University（哈瑟尔特大学）；University of Ngaoundere（恩冈德雷大学）；Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University（斯泰伦博斯大学瓦伦伯格高级研究院（STIAS））；CNRS, Université de Lille, Centrale Lille, Université Polytechnique Hauts-de-France（法国国家科学研究中心、里尔大学、中央里尔学院、上法兰西理工学院）
Recently, we have shown how the phase of an electromagnetic field can be determined by measuring the population of either of the two states of a two-level atomic system excited by this field, via the so-called Bloch-Siegert oscillation resulting from the interference between the co- and counter-rotating excitations. Here, we show how a degenerate entanglement, created without transmitting any timing signal, can be used to teleport this phase information. This phase-teleportation process may be applied to achieve frequency-locking of remote oscillators, thereby facilitating the process of synch…
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…
Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even …
Quantum networking based on optical Gaussian states, although promising in terms of scalability, is hindered by the fact that their entanglement cannot be distilled via Gaussian operations. We show that optomechanics, integrable (on-chip) availability, and particularly the scope to measure the mechanical degree of freedom, can address this problem. Here, one of the optical modes of a two-mode squeezed vacuum is injected into a single-sided Fabry-Pérot cavity and non-linearly coupled to a mechanical oscillator. Afterward, the position of the oscillator is measured using pulsed optomechanics and…
We experimentally demonstrate storage and on-demand release of phase-sensitive, photon-number superposition states of the form $α|0\rangle + βe^{iθ} |1\rangle$ for an optical quantized oscillator mode. For this purpose, we introduce a phase-probing mechanism to a storage system composed of two concatenated optical cavities, which was previously employed for storage of phase-insensitive single-photon states [Phys. Rev. X 3, 041028 (2013)]. This is the first demonstration of all-optically storing highly nonclassical and phase-sensitive quantum states of light. The strong nonclassicality of the s…
We analyze theoretically how to use the radiation pressure coupling between a mechanical oscillator and an optical cavity field to generate in a heralded way a single quantum of mechanical motion (a Fock state), and release on-demand the stored excitation as a single photon. Starting with the oscillator close to its ground state, a laser pumping the upper motional sideband leads to dynamical backaction amplification and to the creation of correlated photon-phonon pairs. The detection of one Stokes photon thus projects the macroscopic oscillator into a single-phonon Fock state. The non-classica…
We study theoretically a three-mode optomechanical system where two mechanical oscillators are independently coupled to a single cavity mode. By optimized two-tone or four-tone driving of the cavity one can prepare the mechanical oscillators in an entangled two-mode squeezed state, even if they start in a thermal state. The highly-pure, symmetric steady-state achieved allows the optimal fidelity of standard continuous-variable teleportation protocols to be achieved. In contrast to other reservoir engineering approaches to generating mechanical entanglement, only a single reservoir is required …
The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many physical qubits, but can also be realized using a single higher-dimensional quantum system, such as a harmonic oscillator. A powerful encoding is formed from a periodically spaced superposition of position eigenstates. Various proposals have been made for realizing approximations to such states, but these have thus far remained out of reach. Here, we demonstra…
We use the uncertainty relation between the operators associated to the total number of particles and to the relative phase of two bosonic modes to construct entanglement and Einstein-Podolsky-Rosen steering criteria. These can be tested experimentally in a variety of systems, such as optical fields, Bose-Einstein condensates or mechanical oscillators. While known entanglement criteria involving the phase observable typically require to perform interference measurements by recombining the two systems, our criteria can be tested through local measurements at two spatially distinct positions, to…
Mechanical systems facilitate the development of a new generation of hybrid quantum technology comprising electrical, optical, atomic and acoustic degrees of freedom. Entanglement is the essential resource that defines this new paradigm of quantum enabled devices. Continuous variable (CV) entangled fields, known as Einstein-Podolsky-Rosen (EPR) states, are spatially separated two-mode squeezed states that can be used to implement quantum teleportation and quantum communication. In the optical domain, EPR states are typically generated using nondegenerate optical amplifiers and at microwave fre…
Multi-color entangled states of light including low-loss optical fiber transmission and atomic resonance frequencies are essential resources for future quantum information network. We present the experimental achievement on the three-color entanglement generation at 852 nm, 1550 nm and 1440 nm wavelengths for optical continuous variables. The entanglement generation system consists of two cascaded non-degenerated optical parametric oscillators (NOPOs). The flexible selectivity of nonlinear crystals in the two NOPOs and the tunable property of NOPO provide large freedom for the frequency select…
We report the generation of a type-I multimode two-photon state on a rubidium D$_2$ line (780 nm) using periodically poled KTiOPO$_4$ crystals. With a degenerate optical parametric oscillator far below threshold, we observe an oscillatory correlation function, the cross-correlation between two photons shows a cavity bandwidth of about 7.8 MHz. We also use a Fabry-P$\acute{\rm{e}}$rot etalon to filter its most longitudinal modes and observe its time correlation function. The experimental data are well fitted to theoretical curves. This system could be utilized for demonstrating storage and retr…
Coherent inter-conversion between an optical and a mechanical excitation in an optomechanical resonator can be used for the storage of an optical pulse as an excitation in a mechanical oscillator. This optomechanical light storage is enabled by external writing and readout pulses at one mechanical frequency below the optical resonance. In this paper, we expand an earlier experimental study [Phys. Rev. Lett. 107, 133601 (2011)] on storing an optical pulse as a radial breathing mode in a silica microsphere. We show that the heterodyne beating between a readout pulse and the corresponding retriev…
The time evolution of occupation number is studied for fermionic or bosonic oscillator linearly fully coupled to several fermionic and bosonic heat baths. The influence of characteristics of thermal reservoirs of different statistics on the non-stationary population probability is analyzed at large times. Applications of the absence of equilibrium in such systems for creating a dynamic (nonstationary) memory storage are discussed.
We report experimental storage and retrieval of weak coherent states of light at telecommunication wavelengths using erbium ions doped into a solid. We use two photon echo based quantum storage protocols. The first one is based on controlled reversible inhomogeneous broadening (CRIB). It allows the retrieval of the light on demand by controlling the collective atomic coherence with an external electric field, via the linear Stark effect. We study how atoms in the excited state affect the signal to noise ratio of the CRIB memory. Additionally we show how CRIB can be used to modify the temporal …
We present a quantum electrical circuit with Josephson junctions formed of two anharmonic oscillators coupled with an interaction $gγ_{1}^{2}γ_{2}^{2}$ where $γ_{1}$ and $γ_{2}$ are position-like coordinates. This type of coupling allows the quantum non-demolition measurement of the energy of one oscillator by monitoring the frequency of the second oscillator. Despite the fundamental tradeoff between the coupling strength $g$ and maximum photon storage capacity of the oscillators, it is possible to achieve high fidelity detection of up to 10 photons over time scale of the order of microseconds…
