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 ambient temperatures is feasible with realistic parameters, and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.
Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since a variety of strong highly nonlinear operations are unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, …
Detection of quantum features in mechanical systems at the nanoscale constitutes a challenging task, given the weak interaction with other elements and the available technics. Here we describe how the interaction between two monomodal transmission-line resonators (TLRs) mediated by vibrations of a nano-electromechanical oscillator can be described. This scheme is then employed for quantum non-demolition detection of the number of phonons in the nano-electromechanical oscillator through a direct current measurement in the output of one of the TLRs. For that to be possible an undepleted field in…
We consider two separated oscillators initially in equilibrium and continuously interacting with thermal environments, and propose a way to entangle them using a mediating qubit. An appropriate interaction allows for an analytic treatment of the open system, removes the necessity of fine-tuning interaction times and results in a high tolerance of the entanglement to finite temperature. The entanglement thus produced between the oscillators can be verified either through a Bell inequality relying on oscillator parity measurements or through conditional extraction of the entanglement on to two m…
Optical squeezing mediated by levitated oscillators at their quantum ground state
CNR-INO（意大利国家研究委员会红外光学研究所）；Dipartimento di Fisica e Astronomia, Univ. Di Firenze（佛罗伦萨大学物理与天文系）；INFN, Sezione di Firenze（意大利国家核物理研究院佛罗伦萨分部）；European Laboratory for Non-Linear Spectroscopy (LENS)（欧洲非线性光谱学实验室）
Engineering strong interactions between quantum systems is essential for many phenomena of quantum physics and technology. Typically, strong coupling relies on short-range forces or on placing the systems in high-quality electromagnetic resonators, restricting the range of the coupling to small distances. We use a free-space laser beam to strongly couple a collective atomic spin and a micromechanical membrane over a distance of one meter in a room-temperature environment. The coupling is highly tunable and allows the observation of normal-mode splitting, coherent energy exchange oscillations, …
Remote entanglement of massive oscillators via wire-mediated Coulomb interaction
Technical University of Vienna（维也纳工业大学）；Institute for Theoretical Physics and Vienna Center for Quantum Science and Technology, Technical University of Vienna（维也纳大学理论物理研究所与维也纳量子科学与技术中心）；Institute of Science and Technology Austria（奥地利科学技术研究所）
We show that an atom can be coupled to a mechanical oscillator via quantum vacuum fluctuations of a cavity field enabling energy transfer processes between them. In a hybrid quantum system consisting of a cavity resonator with a movable mirror and an atom, these processes are dominated by two pair-creation mechanisms: the counterrotating (atom-cavity system) and dynamical Casimir interaction terms (optomechanical system). Because of these two pair-creation mechanisms, the resonant atom-mirror coupling is the result of high-order virtual processes with different transition paths well described …
Two close parallel mirrors attract due to a small force (Casimir effect) originating from the electromagnetic quantum vacuum uctuations of the electromagnetic field. These vacuum uctuations can also induce motional forces exerted upon one mirror when the other one moves. Here we consider an optomechanical system consisting of two vibrating mirrors coupled to an optical resonator. We find that motional forces can determine noticeable coupling rates between the two spatially separated vibrating mirrors. We show that, by tuning the two mechanical oscillators into resonance, energy is exchanged be…
We propose a solid-state hybrid platform based on an array of implanted nitrogen-vacancy (NV) centers in diamond magnetically coupled to a mechanical oscillator. The mechanical oscillator and the NV electronic spins both act as a quantum bus and allow us to induce an effective long-range interaction between distant nuclear spins, relaxing the requirements on their spatial distance. The coherent nuclear spin-spin interaction, having the form of an Ising model, can be maintained in the presence of mechanical damping and spin dephasing via a pulsed dynamical decoupling of the nuclear spins in add…
We present the measurement of entanglement between twin beams generated with a doubly resonant optical parameter oscillator (OPO) based on four-wave mixing in hot $^{85}$Rb vapor above threshold. This is the first measurement of entanglement in an OPO with $χ^{(3)}$ media above threshold. We reconstruct the covariance matrix for several configurations and with a full picture of the four side band mode state, we study entanglement between all possible bi-partitions. We show a robust generation of entanglement with stronger generation for a specific pair of modes. For this system, we show that a…
A complex quantum system can be constructed by coupling simple quantum elements to one another. For example, trapped-ion or superconducting quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively quantum objects can be coupled by the exchange of real photons, particularly when driven within resonators that amplify interactions with a single electro-magnetic mode. However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised. Here, we realize phase-coherent int…
We study the non-equilibrium dynamics of two coupled mechanical oscillators with general linear couplings to two uncorrelated thermal baths at temperatures $T_1$ and $T_2$, respectively. We obtain the complete solution of the Heisenberg-Langevin equations, which reveal a coherent mixing among the normal modes of the oscillators as a consequence of their off-diagonal couplings to the baths. Unique renormalization aspects resulting from this mixing are discussed. Diagonal and off-diagonal (coherence) correlation functions are obtained analytically in the case of strictly Ohmic baths with differe…
Mediated Transmission of Quantum Synchronization in Star Networks
Renmin University of China（中国人民大学）；School of Physics, Renmin University of China（中国人民大学物理学院）；Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China（中国人民大学量子态构建与操控教育部重点实验室）
Microelectromechanical systems and integrated photonics provide the basis for many reliable and compact circuit elements in modern communication systems. Electro-opto-mechanical devices are currently one of the leading approaches to realize ultra-sensitive, low-loss transducers for an emerging quantum information technology. Here we present an on-chip microwave frequency converter based on a planar aluminum on silicon nitride platform that is compatible with slot-mode coupled photonic crystal cavities. We show efficient frequency conversion between two propagating microwave modes mediated by t…
We present the first measurement of two-mode squeezing between the twin beams produced by a doubly resonant optical parameter oscillator (OPO) in above threshold operation, based on parametric amplification by non degenerate four wave mixing with rubidium $^{85}$Rb. We demonstrate a maximum intensity difference squeezing of -2.7 dB (-3,5 dB corrected for losses) with a pump power of 285 mW and an output power of 12 mW for each beam, operating close to the D1 line of Rb atoms. The possibility to use open cavities combined with the high gain media can provide a strong level of noise compression,…
The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.
We theoretically investigate two quantum modes interacting via local couplings to a dissipative field. Our model considers two mechanical modes with distinct frequencies coupled optomechanically to the same cavity mode. The dissipative cavity field mediates the interaction between the mechanical modes but also leads to decoherence of the mechanical oscillators. Depending on the ratio between effective interaction strength and dissipation rate, which can be chosen via the pump detuning, the interaction assumes a quantum mechanical or classical character. For any cavity decay, there is a regime …
We present a brief critical review of the proposals for quantum computation with trapped ions, with particular emphasis on the possibilities for quantum computation without the need for cooling to the quantum ground state of the ions' collective oscillatory modes.
Carnot established in 1824 that the efficiency of cyclic engines operating between a hot bath at absolute temperature $T_{hot}$ and a bath at a lower temperature $T_{cold}$ cannot exceed $1-T_{cold}/T_{hot}$. We show that linear oscillators alternately in contact with hot and cold baths obey this principle in the quantum as well as in the classical regime. The expression of the work performed is derived from a simple prescription. Reversible and non-reversible cycles are illustrated. The paper begins with historical considerations and is essentially self-contained.
We present exact solutions for the quantum time evolution of two spatially separated, local inductor-capacitor (LC) oscillators that are coupled optomechanically to a long elastic strip that functions as a quantum thermal acoustic field environment. We show that the optomechanical coupling to the acoustic environment gives rise to causal entanglement dynamics between the two LC oscillators in the absence of resonant photon exchange between them, and that significant entanglement develops regardless of the environment temperature. Such a process establishes that distributed entanglement may be …
The possibility of maintaining entanglement in a quantum system at finite, even high, temperatures -- the so-called `hot entanglement' -- has obvious practical interest, but also requires closer theoretical scrutiny. Since quantum entanglement in a system evolves in time and is continuously subjected to environmental degradation, a nonequilibrium description by way of open quantum systems is called for. To identify the key issues and the contributing factors that may permit `hot entanglement' to exist, or the lack thereof, we carry out a model study of two spatially-separated, coupled oscillat…
In this paper we give a first principles microphysics derivation of the nonequilibrium forces between an atom, treated as a three dimensional harmonic oscillator, and a bulk dielectric medium modeled as a continuous lattice of oscillators coupled to a reservoir. We assume no direct interaction between the atom and the medium but there exist mutual influences transmitted via a common electromagnetic field. By employing concepts and techniques of open quantum systems we introduce coarse-graining to the physical variables - the medium, the quantum field and the atom's internal degrees of freedom,…
We present that two spin defects (SDs) can be entangled through a magnon polariton mode, within the strong coupling regime. The magnonic modes are provided by an antiferromagnetic (AF) MnF$_{2}$ layer and their dispersion is characterized by the layer's thickness. The macroscopic quantum electrodynamics theory is used to describe the light-matter interactions, where the Green's functions are its core element. The individual SD relaxes by exciting the magnon polariton modes, exhibiting high enhancement values of the Purcell factor. When two SDs are considered, an oscillatory population exchange…
Optical entanglement facilitated by a hot mechanical oscillator
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科大学物理系）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Faculty of Physics, Branch of M.V. Lomonosov Moscow State University in Baku（莫斯科大学巴库分校物理系）
We investigate the quantum entanglement dynamics of undriven anharmonic (nonlinear) oscillators with quartic potentials. We first consider the indirect interaction between two such nonlinear oscillators mediated by a third, linear oscillator and show that it leads to a time-varying entanglement of the oscillators, the entanglement being strongly influenced by the nonlinear oscillator dynamics. In the presence of dissipation, the role of nonlinearity is strongly manifested in the steady state dynamics of the indirectly coupled anharmonic oscillators. We further illustrate the effect of nonlinea…
We study all known and as yet unknown forces between two neutral atoms, modeled as three dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center of mass motion of the atom, its internal degrees of freedom and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first principle, systematic and unified description including the intrinsic field fluctuations and induced dipole fluctuations. The inclusi…
We study the laser cooling of a mechanical oscillator through the coupling with a dissipative three-level system. Under a background temperature beyond the Lamb-Dicke regime, we extend the standard cooling analysis by separately studying the classical motion and the quantum dynamics of the oscillator. In Ladder-system cooling, the cooling rate degrades by orders of magnitude at large classical motion. This phenomenon causes a critical transition of the final temperature at a hot background. In stark contrast, electromagnetic-induced-transparency (EIT) cooling with a $Λ$-system produces signifi…
We propose and analyze a setup to achieve strong coupling between a single trapped atom and a mechanical oscillator. The interaction between the motion of the atom and the mechanical oscillator is mediated by a quantized light field in a laser driven high-finesse cavity. In particular, we show that high fidelity transfer of quantum states between the atom and the mechanical oscillator is in reach for existing or near future experimental parameters. Our setup provides the basic toolbox for coherent manipulation, preparation and measurement of micro- and nanomechanical oscillators via the tools …
Control over the quantum states of a massive oscillator is important for several technological applications and to test the fundamental limits of quantum mechanics. Addition of an internal degree of freedom to the oscillator could be a valuable resource for such control. Recently, hybrid electromechanical systems using superconducting qubits, based on electric-charge mediated coupling, have been quite successful. Here, we realize a hybrid device, consisting of a superconducting transmon qubit and a mechanical resonator coupled using the magnetic-flux. The coupling stems from the quantum-interf…
We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which allows to couple the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benefit from the rich toolbox of quantum control over internal atomic states. Previous schemes i…
Autonomous quantum thermal machines do not require an external coherent drive or work input to perform the desired tasks, which makes them a promising candidate for thermal management in quantum systems. Here, we propose an autonomous quantum thermal machine in which two uncoupled macroscopic mechanical resonators or microwave resonators achieve considerable entanglement via a hot thermal bath. This becomes possible by coupling the resonators to a common two-level system or third harmonic oscillator and driving it by the hot incoherent thermal bath. The critical step to make the entanglement i…
We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two level systems and quantum harmonic oscillators. In particular, we study energy transfer processes from a given quantum system, termed charger, to another one, i.e. the proper battery. In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by prope…
We predict the existence of the electromagnetically induced absorption (EIA) in the double cavity configurations of the hybrid opto-electro mechanical systems (OEMS). We discuss the origin of the EIA in OEMS which exhibit the existence of an absorption peak within the transparency window. We provide analytical results for the width and the height of the EIA peak. The combination of the EIT and EIA is especially useful for photon switching applications. The EIA that we discuss is different from the one originally discovered by Lezama et al in atomic systems and can be understood in terms of the…
We show that, in the gapless Kondo Regime, a single local quench at one end of a Kondo spin chain induces a fast and long lived oscillatory dynamics. This quickly establishes a high quality entanglement between the spins at the opposite ends of the chain. This entanglement is mediated by the Kondo Cloud, attains a constant high value independent of the length for large chains, and shows thermal robustness. In contrast, when the Kondo cloud is absent, e.g. in the gapped dimer regime, only finite size end to end effects can create some entanglement on a much longer time-scale for rather short ch…
Two defect particles that couple to a harmonic chain, acting as common reservoir, can become entangled even when the two defects do not directly interact and the harmonic chain is effectively a thermal reservoir for each individual defect. This dynamics is encountered for sufficiently low temperatures of the chain and depends on the initial state of the two oscillators. In particular, when each defect is prepared in a squeezed state, entanglement can be found at time scales at which the steady state of a single defect is reached. We provide a microscopic description of the coupled quantum dyna…
Classically, the tendency towards spontaneous synchronization is strongest if the natural frequencies of the self-oscillators are as close as possible. We show that this wisdom fails in the deep quantum regime, where the uncertainty of amplitude narrows down to the level of single quanta. Under these circumstances identical self-oscillators cannot synchronize and detuning their frequencies can actually help synchronization. The effect can be understood in a simple picture: Interaction requires an exchange of energy. In the quantum regime, the possible quanta of energy are discrete. If the extr…
We study stationary entanglement among three harmonic oscillators which are dipole coupled to a one-dimensional or a three-dimensional bosonic environment. The analysis of the open-system dynamics is performed with generalized quantum Langevin equations which we solve exactly in Fourier representation. The focus lies on Gaussian bipartite and tripartite entanglement induced by the highly non-Markovian interaction mediated by the environment. This environment-induced interaction represents an effective many-parties interaction with a spatial long-range feature: a main finding is that the presen…
We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.
Cavity-enhanced radiation pressure coupling between optical and mechanical degrees of freedom allows quantum-limited position measurements and gives rise to dynamical backaction enabling amplification and cooling of mechanical motion. Here we demonstrate purely dispersive coupling of high Q nanomechanical oscillators to an ultra-high finesse optical microresonator via its evanescent field, extending cavity optomechanics to nanomechanical oscillators. Dynamical backaction mediated by the optical dipole force is observed, leading to laser-like coherent nanomechanical oscillations solely due to r…
A broad family of phase transitions in the closed as well as open quantum systems is known to be mediated by a non-Hermitian degeneracy (a.k.a. exceptional point, EP) of the Hamiltonian. In the EP limit, in general, the merger of an $N-$plet of the energy eigenvalues is accompanied by a parallel (though not necessarily complete) degeneracy of eigenstates (forming an EP-asociated $K-$plet; in mathematics, $K$ is called the geometric multiplicity of the EP). In the literature, unfortunately, only the benchmark matrix models with $K=1$ can be found. In our paper the gap is filled: the EP-mediated…
The non-equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation-dissipation theorem is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero-point fluctuation…
