We consider the problem of whether the canonical and microcanonical ensembles are locally equivalent for short-ranged quantum Hamiltonians of $N$ spins arranged on a $d$-dimensional lattices. For any temperature for which the system has a finite correlation length, we prove that the canonical and microcanonical state are approximately equal on regions containing up to $O(N^{1/(d+1)})$ spins. The proof rests on a variant of the Berry--Esseen theorem for quantum lattice systems and ideas from quantum information theory.
The two criteria of ensemble equivalence, i.e. the macrostate equivalence and the measure equivalence, are investigated for a general pair of states. The macrostate equivalence implies the two ensembles are indistinguishable by the measurement of macroscopic quantities obeying the large-deviation principle, and the measure equivalence means that the specific relative entropy of these two states vanishes in the thermodynamic limit. It is shown that the measure equivalence implies the macrostate equivalence for a general pair of states by deriving an inequality connecting the large-deviation rat…
It is typically assumed, without justification, that a weak coupling between a system and a bath is a necessary condition for the equivalence of a canonical ensemble and a microcanonical ensemble. For instance, in a canonical ensemble, temperature emerges if the system and the bath are uncoupled or weakly coupled. We investigate the validity region of this weak coupling approximation, using a coupled composite-spin system. Our results show that the spin coupling strength can be as large as the level spacing of the system, indicating that the weak coupling approximation has a much wider region …
The equivalence of thermodynamic ensembles is at the heart of statistical mechanics and central to our understanding of equilibrium states of matter. Recently, it has been shown that there is a formal connection between the dynamics of open quantum systems and the statistical mechanics in an extra dimension. This is established through the fact that an open system dynamics generates a Matrix Product state (MPS) which encodes the set of all possible quantum jump trajectories and permits the construction of generating functions in the spirit of thermodynamic partition functions. In the case of c…
We study a quantum spin system on the $d$-dimensional hypercubic lattice $Λ$ with $N=L^d$ sites with periodic boundary conditions. We take an arbitrary translation invariant short-ranged Hamiltonian. For this system, we consider both the canonical ensemble with inverse temperature $β_0$ and the microcanonical ensemble with the corresponding energy $U_N(β_0)$. For an arbitrary self-adjoint operator $\hat{A}$ whose support is contained in a hypercubic block $B$ inside $Λ$, we prove that the expectation values of $\hat{A}$ with respect to these two ensembles are close to each other for large $N$ …
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body observables is restricted by a Gaussian concentration bound (or Chernoff--Hoeffding inequality) above some threshold temperature. This bound is then derived for arbitrary Gibbs states of systems that include long-range interactions Secondly, we establish a quantitative relationship between the concentration bound of the Gibbs state and the equivalence of can…
We present a quantum memory protocol that allows to store light in ensembles of two-level atoms, e.g. rare-earth ions doped into a crystal, by modulating the refractive index of the host medium of the atoms linearly in time. We show that under certain conditions the resulting dynamics is equivalent to that underlying the gradient echo memory protocol, which relies on a spatial gradient of the atomic resonance frequencies. We discuss the prospects for an experimental implementation.
We study a hybrid nano-mechanical system coupled to a spin ensemble as a quantum simulator to favor a quantum interference effect, the electromagnetically induced transparency (EIT). This system consists of two nano-mechanical resonators (NAMRs), each of which coupled to a nuclear spin ensemble. It could be regarded as a crucial element in the quantum network of NAMR arrays coupled to spin ensembles. Here, the nuclear spin ensembles behave as a long-lived transducer to store and transfer the NAMRs' quantum information. This system shows the analog of EIT effect under the driving of a probe mic…
Phase synchronization refers to a kind of collective phenomenon that the phase difference between two or more systems is locked, and it has widely been investigated between systems with the identical physical properties, such as the synchronization between mechanical oscillators and the synchronization between atomic ensembles. Here, we investigate the synchronization behavior between the mechanical oscillator and the atomic ensemble, the systems with different physical properties, and observe a novel synchronization phenomenon, i.e., the phase sum, instead of phase difference, is locked. We r…
We propose a protocol to dissipatively cool a room temperature mechanical resonator using a nitrogen-vacancy (NV) center ensemble. The spin ensemble is coupled to the resonator through its orbitally-averaged excited state, which has a spin-strain interaction that has not been previously characterized. We experimentally demonstrate that the spin-strain coupling in the excited state is $13.5\pm0.5$ times stronger than the ground state spin-strain coupling. We then theoretically show that this interaction combined with a high-density spin ensemble enables the cooling of a mechanical resonator fro…
We study the effect of large acceleration of an uniformly accelerated frame on the validity of weak equivalence principle. Specifically we demonstrate how the behaviour of free quantum particle, as observed by an observer with large uniform acceleration, completely changes from that of a quantum particle emmarsed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen fro…
We propose a scheme for the generation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in the highly unresolved sideband (HURSB) regime where the decay rate of cavity is much larger than the frequency of the mechanical oscillator. The system is formed by two two-level atomic ensembles and an optomechanical system with cavity driven by two lasers with different amplitudes. In the HURSB regime, the squeezing of the movable mirror can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is put into the optomechanical system. However, if two atom…
We investigate eigenstate thermalization from the point of view of vanishing particle and heat currents between a few-body fermionic Hamiltonian prepared in one of its eigenstates and an external, weakly coupled Fermi-Dirac gas. The latter acts as a thermometric probe, with its temperature and chemical potential set so that there is neither particle nor heat current between the two subsystems. We argue that the probe temperature can be attributed to the few-fermion eigenstate in the sense that (i) it varies smoothly with energy from eigenstate to eigenstate, (ii) it is equal to the temperature…
We demonstrate that optomechanical non-reciprocity is equivalent to the anti-resonance, often discussed in the context of coupled driven harmonic oscillators. We show that that suitable phase-difference between the cavity driving fields make the relevant optomechanical couplings complex, which leads to non-reciprocity in the field fluctuations and anti-resonance in average field amplitudes. This analogy with anti-resonance demonstrates that only for a particular frequency (the so-called isolation frequency) of input signal, maximum non-reciprocity can be achieved. In contrast to the previous s…
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…
Coherent control of the nitrogen-vacancy (NV) center in diamond's triplet spin state has traditionally been accomplished with resonant ac magnetic fields under the constraint of the magnetic dipole selection rule, which forbids direct control of the $|-1>\leftrightarrow |+1>$ spin transition. We show that high-frequency stress resonant with the spin state splitting can coherently control NV center spins within this subspace. Using a bulk-mode mechanical microresonator fabricated from single-crystal diamond, we apply intense ac stress to the diamond substrate and observe mechanically driven Rab…
We consider quantum ensembles which are determined by pre- and post-selection. Unlike the case of only pre-selected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain non-trivial bi-partite ensembles which do satisfy causality. These ensembles give rise to a violation of the CHSH inequality, which exceeds the maximal quantum violation given by Tsirelson's bound, $B_{\…
In diamond, the mechanical vibration induced strain can lead to interaction between the mechanical mode and the nitrogen-vecancy (NV) centers. In this work, we propose to utilize the strain induced coupling for the quantum non-demolition (QND) single phonon measurement and memory in diamond. The single phonon in a diamond mechanical resonator can be perfectly absorbed and emitted by the NV centers ensemble (NVE) with adiabatically tuning the microwave driving. An optical laser drives the NVE to the excited states, which have much larger coupling strength to the mechanical mode. By adiabaticall…
The quantum nature of bulk ensemble NMR quantum computing --the center of recent heated debate, is addressed. Concepts of the mixed state and entanglement are examined, and the data in a 2 qubit liquid NMR quantum computation are analyzed. It is pointed out that the key problem in the current debate is the understanding of entanglement in a mixed state system. The following points are concluded in this Letter: 1)Density matrix describes the "state" of an average particle in an ensemble. It can not describe the state of an individual particle in an ensemble in detail; 2) Entanglement is a prope…
Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of $5.9~\text{dB}$ for $20$ spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for $20$ spins with a fidelity of $\sim 0.62$ at cryogenic temperature. The numerical simulations show th…
We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these repre…
In this work the induced van der Waals interaction between a pair of neutral atoms or molecules is considered by use of a statistical mechanical method. Commonly this interaction is obtained by standard quantum mechanical perturbation theory to second order. However, the latter is restricted to electrostatic interactions between charges and dipole moments. So with radiating dipole-dipole interaction where retardation effects are important for large separations of the particles, other methods are needed, and the resulting induced interaction is the Casimir-Polder interaction usually obtained by…
We propose a potentially practical scheme for realization of two-mode squeezed state with respect to two distant nitrogen-vacancy center ensembles coupled to two interconnected mechanical modes of diamond nanoresonators. By making use of the tunable phonon-spin interaction and the engineered phonon-phonon tunneling, both the desired excitation transfer process and the optimal two-mode squeezing between spin ensembles can be realized. We investigate the dynamics of the total system under infulences from the mechanical decay using both analytical and numerical methods, where the realistic condit…
We study the optical bistability of an optomechanical system in which the position of a mechanical oscillator modulates the cavity frequency. The steady-state mean-field equation of the optical mode is identical to the one for a Kerr medium, and thus we expect it to have the same characteristic behavior with a lower, a middle, and an upper branch. However, the presence of position fluctuations of the mechanical resonator leads to a new feature: the upper branch will become unstable at sufficiently strong driving in certain parameter regimes. We identify the appropriate parameter regime for the…
Ensembles of quantum mechanical spins offer a promising platform for quantum memories, but proper functionality requires accurate control of unavoidable system imperfections. We present an efficient control scheme for a spin ensemble strongly coupled to a single-mode cavity based on a set of Volterra equations relying solely on weak classical control pulses. The viability of our approach is demonstrated in terms of explicit storage and readout sequences that will serve as a starting point towards the realization of more demanding full quantum mechanical optimal control schemes.
We present computable criterion for completely classifying multi-qubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multi-qubit systems are local unitary equivalent or not. Once obtaining the positive answer, we are further able to compute the corresponding unitary operators precisely. Since the scheme is based on the mean values of some quantum mechanical observables, it supplies an experimental way to judge the local equivalence of quantum states.
We consider a hybrid optomechanical system which is composed of the atomic ensemble and a standard optomechanical cavity driven by the periodically modulated external laser field. We investigate the asymptotic behaviors of Heisenberg operator first moments and clearly show the approaching process between the exact numerical results and analytical solutions. Based on the specific modulation forms of external driving and effective optomechanical coupling, we discuss in detail the atom-mirror entanglement enhancement, respectively. Compared with the constant driving regime, the entanglement can b…
We analyze a quantum force sensor that uses coherent quantum noise cancellation (CQNC) to beat the Standard Quantum Limit (SQL). This sensor, which allows for the continuous, broad-band detection of feeble forces, is a hybrid dual-cavity system comprised of a mesoscopic mechanical resonator optically coupled to an ensemble of ultracold atoms. In contrast to the stringent constraints on dissipation typically associated with purely optical schemes of CQNC, the dissipation rate of the mechanical resonator only needs to be matched to the decoherence rate of the atomic ensemble -- a condition that …
We suggest to interface nanomechanical systems via an optical quantum bus to atomic ensembles, for which means of high precision state preparation, manipulation and measurement are available. This allows in particular for a Quantum Non-Demolition Bell measurement, projecting the coupled system, atomic ensemble - nanomechanical resonator, into an entangled EPR-state. The entanglement is observable even for nanoresonators initially well above their ground states and can be utilized for teleportation of states from an atomic ensemble to the mechanical system.
We show that differently constructed ensembles having the same density matrix may be physically distinguished by observing fluctuations of some observables. An explicit expression for fluctuations of an observable in an ensemble is given. This result challenges Peres's fundamental postulate and seems to be contrary to the widely-spread belief that ensembles with the same density matrix are physically identical. This leads us to suggest that the current liquid NMR quantum computing is truly quantum-mechanical in nature.
An expression is proposed for the quantum mechanical state of a pre- and post-selected ensemble, which is an ensemble determined by the final as well as the initial state of the quantum systems involved. It is shown that the probabilities calculated from the proposed state agree with previous expressions, for cases where they both apply. The same probabilities are found when they are calculated in the forward- or reverse-time directions. This work was prompted by several problems raised by Shimony recently in relation to the state, and time symmetry, of pre- and post-selected ensembles.
We predict ground state cooling of a micro-mechanical oscillator, i.e. a vibrating end-mirror of an optical cavity, by resonant coupling of mirror vibrations to a narrow internal optical transition of an ensemble of two level systems. The particles represented by a collective mesoscopic spin model implement, together with the cavity, an efficient, frequency tailorable zero temperature loss channel which can be turned to a gain channel of pump. As opposed to the case of resolved-sideband cavity cooling requiring a small cavity linewidth, one can work here with low finesses and very small cavity…
We point out that the bootstrap program in quantum mechanics proposed by Han et al reduces to a bootstrap study of a microcanonical ensemble of the same Hamiltonian in the $\hbar \to 0$ limit. In the limit, the quantum mechanical archipelago becomes an extremely thin line for an anharmonic oscillator. For a double-well potential, a peninsula in $E\le 0$ appears.
We investigate theoretically the effect of optical feedback from a cavity containing an ultracold two level atomic ensemble, on the bistable behavior shown by mean intracavity optical field in an optomechanical cavity resonator. It turns out that the optical bistability can be controlled by tuning the frequency and power of the driving laser and is largely affected by the presence of the atomic ensemble in the feedback cavity. In essence, our work emphasizes the possibility of realization of a controllable optical switch depending on the hybrid interaction, commanding lower threshold power tha…
We investigate a hybrid electro-mechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg transition and the mechanics allows cooling to its motional ground state with a single atom despite the considerable mass imbalance between the two subsystems. We show that the rich electronic spectrum of Rydberg atoms, combined with their high degree of optical control, paves the way towards implementing various quantum-control protocol for the mechanical oscilla…
Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble
Macau University of Science and Technology（澳门科技大学）；New Jersey Institute of Technology（新泽西理工学院）；Foshan University（佛山大学）；University of Surrey（萨里大学）；South China Agricultural University（华南农业大学）
The mechanical influence on objects due to their interaction with light has been a central topic in atomic physics for decades. Thus, one finds that many concepts developed to describe cavity optomechanical systems with solid-state mechanical oscillators have also been developed in parallel in relation to cold atomic physics. I describe several of these ideas from atomic physics, including optical methods for detecting quantum states of single cold atoms and atomic ensembles, motional effects within single-atom cavity quantum electrodynamics, and collective optical effects such as superradiant…
