While it has been possible to build fields in high-Q cavities with a high degree of squeezing for some years, the engineering of arbitrary squeezed states in these cavities has only recently been addressed [Phys. Rev. A 68, 061801(R) (2003)]. The present work examines the question of how to squeeze any given cavity-field state and, particularly, how to generate the squeezed displaced number state and the squeezed macroscopic quantum superposition in a high-Q cavity.
To achieve high degree of quantum noise squeezing, an optical cavity is often employed to enhance the interaction time between light and matter. Here, we propose to utilize the effect of coherent population trapping (CPT) to directly generate squeezed light without any optical cavity. Combined with the slow propagation speed of light in a CPT medium, a coherent state passing through an atomic ensemble with a high optical density (OD) can evolve into a highly squeezed state even in a single passage. Our study reveals that noise squeezing of more than $10$ dB can be achieved with an OD of 1,000,…
We present the first experimental observation of quantum fluctuation spectra in two coupled optical cavities with an injected squeezed vacuum light. The quadrature components of the reflected squeezed vacuum spectra are measured by phase sensitive homodyne detector. The experimental results demonstrate coupled-resonator-induced transparency in the quantum regime, in which electromagnetically-induced-transparency-like characteristic of the absorption and dispersion properties of the coupled optical cavities determines the line-shape of the reflected quantum noise spectra.
We investigate the stationary bipartite entanglement is a useful hybrid optomechanical system, which is constituted of two coupled-cavity optomechanics through a photon hopping process and both are driven by squeezed light. The transfer of correlations from an entangled light source to optomechanical cavities is explored. It is found that the generation of bipartite entanglement and entanglement transfer depend strongly on photon hopping strength and the matching of the input squeezed modes to the cavity modes. It is revealed that the generated stationary bipartite entanglement due to squeezed…
We investigate theoretically the properties of squeezed states generated using degenerate parametric down conversion in lossy cavities. We show that the Lindblad master equation, which governs the evolution of this system, has as its solution a squeezed thermal state with an effective temperature and squeezing parameter that depends on time. We derive analytical solutions for the time-evolution of quadrature noise, thermal photon number, squeezing parameter, and total photon number under different pumping regimes. We also find the steady state limits of the quadrature noises and discuss the $ …
We propose and experimentally demonstrate a method for non-invasive measurements of cavity parameters by injection of squeezed vacuum into an optical cavity. The principle behind this technique is the destruction of the correlation between upper and lower quantum sidebands with respect to the carrier frequency when the squeezed field is incident on the cavity. This method is especially useful for ultrahigh $Q$ cavities, such as whispering gallery mode (WGM) cavities, in which absorption and scattering by light-induced nonlinear processes inhibit precise measurements of the cavity parameters. W…
The transfer of entangled, quantum correlated, flying photons from a squeezed field to single-mode cavities is investigated. It is shown that, while the transfer of photons begins immediately after the input squeezed field is turned on, the time at which quantum correlations start to be transferred to the cavities is strongly dependent on the initial population of the cavities. For the initially empty cavities, the transfer of quantum correlations begins immediately after the squeezed field is turned on, but it is delayed by a certain time interval when the cavities are initially populated. We…
We investigate the Hermitian and the non-Hermitian dynamics of the mode entanglement in two identical optical cavities coupled by a chiral mirror. By employing the non-Hermitian quantum evolution, we calculate the logarithmic negativity measure of entanglement for initially Fock, coherent and squeezed states, separately. We verify the non-conservation of mean spin for the initially coherent and squeezed states when the coupling is non-reciprocal and report the associated spin noise for each case. We examine the effects of non-conserved symmetries on the mode correlations and determine the degr…
We show that two-mode squeezed vacuum-like states may be engineered in the Bohm-Madelung formalism by adequately choosing the phase of the wavefunction. The difference between our wavefunction and the one of the squeezed vacuum states is given precisely by the phase we choose.
A scheme is proposed for engineering two-mode squeezed states of two separated cold atomic clouds positioned near the surface of a superconducting stripline resonator. Based on the coherent magnetic coupling between the atomic spins and a stripline resonator mode, the desired two-mode squeezed state can be produced via precisely control on the dynamics of the system. This scheme may be used to realize scalable on-chip quantum networks with cold atoms coupling to stripline resonators.
We show that two qubits can be entangled by local interactions with an entangled two-mode continuous variable state. This is illustrated by the evolution of two two-level atoms interacting with a two-mode squeezed state. Two modes of the squeezed field are injected respectively into two spatially separate cavities and the atoms are then sent into the cavities to resonantly interact with the cavity field. We find that the atoms may be entangled even by a two-mode squeezed state which has been decohered while penetrating into the cavity.
This theoretical proposal investigates how resonant interactions occurring when a harmonic oscillator is fed with a stream of entangled qubits allow us to stabilize squeezed states of the harmonic oscillator. We show that the properties of the squeezed state stabilized by this engineered reservoir, including the squeezing strength, can be tuned at will through the parameters of the "input" qubits, albeit in tradeoff with the convergence rate. We also discuss the influence of the type of entanglement in the input, from a pairwise case to a more widely distributed case. This paper can be read in…
We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models which could be relevant for quantum technology applications. We assume minimal resources, represented by systems described by particle-conserving quadratic Hamiltonians, with a single localized squeezed reservoir. We show that in this way it is possible to prepare, in the steady state, the wide class of pure states which can be generated by applying a generic passive Gaussian transformation on a set of equally squeezed modes. This includes non-trivial multipartite entangled states such as clus…
We propose a method of an improving quality of a ring cavity which is imperfect due to non-unit mirror reflectivity. The method is based on using squeezed states of light pulses illuminating the mirror and gradual homodyne detection of a radiation escaping from the cavity followed by single displacement and single squeezing operation performed on the released state. We discuss contribution of this method in process of storing unknown coherent and known squeezed state and generation of squeezing in the optical ring cavities.
The generation of quantum entanglement of macroscopic or mesoscopic bodies in mechanical motion is generally bounded by the thermal fluctuation exerted by their environments. Here we propose a scheme to establish stationary entanglement between two mechanically oscillating mirrors of a cavity. It is revealed that, by applying a broadband squeezed laser acting as a squeezed-vacuum reservoir to the cavity, a stable entanglement between the mechanical mirrors can be generated. Using the adiabatic elimination and master equation methods, we analytically find that the generated entanglement is esse…
Cavity resonators are promising resources for quantum technology, while native nonlinear interactions for cavities are typically too weak to provide the level of quantum control required to deliver complex targeted operations. Here we investigate a scheme to engineer a target Hamiltonian for photonic cavities using ancilla qubits. By off-resonantly driving dispersively coupled ancilla qubits, we develop an optimized approach to engineering an arbitrary photon-number-dependent (PND) Hamiltonian for the cavities while minimizing the operation errors. The engineered Hamiltonian admits various app…
We investigate an optical scheme to conditionally engineer quantum states using a beam splitter, homodyne detection and a squeezed vacuum as an ancillar state. This scheme is efficient in producing non-Gaussian quantum states such as squeezed single photons and superpositions of coherent states (SCSs). We show that a SCS with well defined parity and high fidelity can be generated from a Fock state of $n\leq4$, and conjecture that this can be generalized for an arbitrary $n$ Fock state. We describe our experimental demonstration of this scheme using coherent input states and measuring experimen…
We report the experimental realization of squeezed quantum states of light, tailored for new applications in quantum communication and metrology. Squeezed states in a broad Fourier frequency band down to 1 Hz has been observed for the first time. Nonclassical properties of light in such a low frequency band is required for high efficiency quantum information storage in electromagnetically induced transparency (EIT) media. The states observed also cover the frequency band of ultra-high precision laser interferometers for gravitational wave detection and can be used to reach the regime of quantu…
We propose a method for building a squeezed vacuum state laser with zero diffusion, which results from the introduction of the reservoir engineering technique into the laser theory. As well as the reservoir engineering, our squeezed vacuum laser demands the construction of an effective atom-field interaction. And by building an isomorphism between the cavity field operators in the effective and the Jaynes-Cummings Hamiltonians, we derive the equations of our effective laser directly from the conventional laser theory. Our method, which is less susceptible to errors than reservoir engineering, …
We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight binding approximation and apply this to a two-cavity system as well as to a coupled resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time dependant cross correlation between the photons in different cavities to …
We study the quantum correlations induced by spontaneous parametric down-conversion (SPDC) of a frequency comb. We derive a theoretical method to find the output state corresponding to a pump with an arbitrary spectral profile. After applying it to the relevant example of a spectrally chirped pump, we run an optimization algorithm to numerically find the pump profiles maximizing some target functions. These include the number of independently squeezed modes and the variances of nullifiers defining cluster states used in many continuous-variable quantum information protocols. To assess the adva…
The interaction of an atomic two-level system and a squeezed vacuum leads to interesting novel effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of phase component of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a 4 pi squeezed vacuum. In this paper we show how to ``engineer'' a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two…
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that $N$ two-level systems (TLSs) located near a one-dimensional waveguide can generate a SS by using the mediation effect of the waveguide. However, a coherent driving on each TLS is used to stabilize the SS, which raises a high requirement for experiments. We here propose a scheme to generate stable SS resorting to neither the spin-spin coupling nor the coherent d…
We demonstrate how an acoustic phonon bath when coupled to a quantum dot with the help of a bichromatic laser field may effectively form a quantum squeezed reservoir. This approach allows to achieve an arbitrary degree of squeezing of the effective reservoir and it incorporates the properties of the reservoir into two parameters, which can be controlled by varying the ratio of the Rabi frequencies of the bichromatic field. It is found that for unequal Rabi frequencies, the effective reservoir may appear as a quantum squeezed field of ordinary or inverted harmonic oscillators. When the Rabi fre…
Iterative $C_Z$-gate-based protocol for squeezed Schrödinger cat state engineering
ITMO University（ITMO大学）；SMARTS-Quanttelecom LLC（SMARTS-Quanttelecom有限责任公司）；Saint-Petersburg State Institute of Technology（圣彼得堡国立技术学院）；Research and Education Center of Photonics and Optical IT, ITMO University（ITMO大学光子学与光学信息技术研究与教育中心）
We study how to control the dynamics of tripartite entanglement among optical cavities using non-Markovian baths. In particular, we demonstrate how the reservoir engineering through the utilization of non-Markovian baths with different types of Lorentzian and ohmic spectral densities can lead to an entanglement survival for longer times and in some cases considerable regain of seemingly lost entanglement. Both of these behaviors indicate a better sustainability of entanglement (in time) compared to the usual Markovian bath situations which assumes a flat spectrum of the bath around the system …
We generate squeezed state of light at 860 nm with a monolithic optical parametric oscillator. The optical parametric oscillator consists of a periodically poled KTiOPO_4 crystal, both ends of which are spherically polished and mirror-coated. We achieve both phase matching and cavity resonance by controlling only the temperature of the crystal. We observe up to -8.0 dB of squeezing with the bandwidth of 142 MHz. Our technique makes it possible to drive many monolithic cavities simultaneously by a single laser. Hence our monolithic optical parametric oscillator is quite suitable to continuous-v…
We propose a scheme to realize the two-axis counter-twisting spin-squeezing Hamiltonian inside an optical cavity with the aid of phase-locked atom-photon coupling. By careful analysis and extensive simulation, we demonstrate that our scheme is robust against dissipation caused by cavity loss and atomic spontaneous emission, and it can achieve significantly higher squeezing than one axis twisting. We further show how our idea can be extended to generate two-mode spin-squeezed states in two coupled cavities. Due to its easy implementation and high tunability, our scheme is experimentally realiza…
Bright squeezed vacuum, a promising tool for quantum information, can be generated by high-gain parametric down-conversion. However, its frequency and angular spectra are typically quite broad, which is undesirable for applications requiring single-mode radiation. We tailor the frequency spectrum of high-gain parametric down-conversion using an SU(1,1) interferometer consisting of two nonlinear crystals with a dispersive medium separating them. The dispersive medium allows us to select a narrow band of the frequency spectrum to be exponentially amplified by high-gain parametric amplification. …
We propose that the squeezed light accompanied by hyperradiance is induced by quantum interference in a linear system consisting of a high quality optical cavity and two coherently driven two-level qubits. When two qubits are placed at the crest and trough of the standing wave in the cavity respectively (i.e., they have the opposite coupling coefficient to the cavity), we show that squeezed light is generated in the hyperradiance regime under the conditions of strong coupling and weak driving. Simultaneously, the Klyshko's criterion alternates up and down at unity when the photon number is eve…
We theoretically investigate the quantum phase transition in the collective systems of qubits in a high-quality cavity, which is driven by a squeezed light. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase tr…
We propose a method of generating unitarily single and two-mode field squeezing in an optical cavity with an atomic cloud. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter that is scaled up by the number of atoms, and realizing degenerate and non-degenerate parametric amplification. By means of the input-output theory we show that ideal squeezed states and perfect squeezing could be approached at the output. The scheme is robust to decoherence processes.
Toward Spectral Engineering of Squeezed Light in High-Gain PDC
Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Institute of Applied Physics, Abbe Center of Photonics（应用物理研究所，阿贝光子学中心）；Heinz Nixdorf Institute, Paderborn University（帕德博恩大学海因茨·诺伊多夫研究所）；Department of Electrical Engineering and Information Technology, Paderborn University（帕德博恩大学电气与信息技术系）；Institute for Photonic Quantum Systems (PhoQS), Paderborn University（帕德博恩大学光子量子系统研究所（PhoQS））；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所 IOF）
We propose and analyze a multi-functional setup consisting of high finesse optical cavities, beam splitters, and phase shifters. The basic scheme projects arbitrary photonic two-mode input states onto the subspace spanned by the product of Fock states |n>|n> with n=0,1,2,.... This protocol does not only provide the possibility to conditionally generate highly entangled photon number states as resource for quantum information protocols but also allows one to test and hence purify this type of quantum states in a communication scenario, which is of great practical importance. The scheme is espec…
We propose a method to produce entangled spin squeezed states of a large number of atoms inside an optical cavity. By illuminating the atoms with bichromatic light, the coupling to the cavity induces pairwise exchange of excitations which entangles the atoms. Unlike most proposals for entangling atoms by cavity QED, our proposal does not require the strong coupling regime g^2/κΓ>> 1, where g is the atom cavity coupling strength, κis the cavity decay rate, and Γis the decay rate of the atoms. In this work the important parameter is Ng^2/κΓ, where N is the number of atoms, and our proposal permi…
Quantum information processing in a modular architecture requires the distribution, stabilization and distillation of entanglement in a qubit network. We present autonomous entanglement stabilization protocols between two superconducting qubits that are coupled to distant cavities. The coupling between cavities is mediated and controlled via a three-wave mixing device that generates either a two-mode squeezed state or a delocalized mode between the remote cavities depending on the pump applied to the mixer. Local drives on the qubits and the cavities steer and maintain the system to the desire…
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 …
We provide a scheme for the generation of controlled entangled number states of Bose-Einstein condensates in multiple wells, and also provide a novel method for the creation of squeezed states without severe adiabatic constraints on barrier heights. The condensate in a multiple well trap can be evolved, starting with a specific initial phase difference between the neighboring wells, to a tunable entangled state or a squeezed state. We propose a general formula for the initial phase difference between the neighboring wells that is valid for any number of wells, even and odd.
An experimentally realizable model based on the interaction between an excited two-level atom and a radiation field inside two quantum electrodynamics cavities is proposed. It consists of sending an excited two-level atom through two serial cavities which contain the radiation field. Hence, the Lindblad master equation described the reduced density matrix of the joint-joint field system inside the cavities is exactly solved in Markovian and non-Markovian regimes. However, the rate of entanglement inherent in the total field-field system are evaluated using various witnesses of entanglement suc…
We show that a thermal reservoir can effectively act as a squeezed reservoir on atoms that are subject to energy-level modulation. For sufficiently fast and strong modulation, for which the rotating-wave-approximation is broken, the resulting squeezing persists at long times. These effects are analyzed by a master equation that is valid beyond the rotating wave approximation. As an example we consider a two-level-atom in a cavity with Lorentzian linewidth, subject to sinusoidal energy modulation. A possible realization of these effects is discussed for Rydberg atoms.
Josephson parametric amplifier (JPA) engineering is a significant component in the quantum two-mode squeezed radar (QTMS), to enhance, for instance, radar performance and the detection range or bandwidth. In this study, we apply quantum theory to a research domain focusing the design of QTMS radar. We apply engineered JPA (EJPA) to enhance the performance of a quantum radar (QR). We investigate the correlation between the signal and idler using and we propose strategies for maintaining entanglement at room temperature. We define the quantum signal-to-noise ratio (SNR) and detection range equat…
The hypothetical axion particle (of unknown mass) is a leading candidate for dark matter (DM). Many experiments search for axions with microwave cavities, where an axion may convert into a cavity photon, leading to a feeble excess in the output power of the cavity. Recent work [Nature 590, 238 (2021)] has demonstrated that injecting squeezed vacuum into the cavity can substantially accelerate the axion search. Here, we go beyond and provide a theoretical framework to leverage the benefits of quantum squeezing in a network setting consisting of many sensor-cavities. By forming a local sensor ne…
We describe a hybrid quantum system composed of a micrometer-size carbon nanotube (CNT) longitudinally coupled to a flux qubit. We demonstrate the usefulness of this device for generating high-fidelity nonclassical states of the CNT via dissipative quantum engineering. Sideband cooling of the CNT to its ground state and generating a squeezed ground state, as a mechanical analogue of the optical squeezed vacuum, are two additional examples of the dissipative quantum engineering studied here. Moreover, we show how to generate a long-lived macroscopically-distinct superposition (i.e., a Schröding…
An experimental demonstration of a non-classical state of a nanomechanical resonator is still an outstanding task. In this paper we show how the resonator can be cooled and driven into a squeezed state by a bichromatic microwave coupling to a charge qubit. The stationary oscillator state exhibits a reduced noise in one of the quadrature components by a factor of 0.5 - 0.2. These values are obtained for a 100 MHz resonator with a Q-value of 10$^4$ to 10$^5$ and for support temperatures of T $\approx$ 25 mK. We show that the coupling to the charge qubit can also be used to detect the squeezed st…
We present a scheme to conditionally engineer an optical quantum system via continuous-variable measurements. This scheme yields high-fidelity squeezed single photon and superposition of coherent states, from input single and two photon Fock states respectively. The input Fock state is interacted with an ancilla squeezed vacuum state using a beam-splitter. We transform the quantum system by post-selecting on the continuous-observable measurement outcome of the ancilla state. We experimentally demonstrate the principles of this scheme using displaced coherent states and measure experimentally f…
We show how to use two-mode squeezed light to exponentially enhance cavity-based dispersive qubit measurement. Our scheme enables true Heisenberg-limited scaling of the measurement, and crucially, is not restricted to small dispersive couplings or unrealistically long measurement times. It involves coupling a qubit dispersively to two cavities, and making use of a symmetry in the dynamics of joint cavity quadratures (a so-called quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme and its robustness against imperfections, as well as a realistic implementation in circui…
A system of two coupled cavities with $N-1$ photons is shown to be dynamically equivalent to an array of $N$ coupled cavities containing one photon. Every transition in the two cavity system has a dual phenomenon in terms of photon transport in the cavity array. This duality is employed to arrive at the required coupling strengths and nonlinearities in the cavity array so that controlled photon transfer is possible between any two cavities. This transfer of photons between two of the cavities in the array is effected without populating the other cavities. The condition for perfect transport en…
We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity QED parameters and with nonideal coupling.
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations resulting in high contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an en…
Quantum measurements of mechanical systems can produce optical squeezing via ponderomotive forces. Its observation requires high environmental isolation and efficient detection, typically achieved by using optical cavities and cryogenic cooling. Here we realize these conditions by measuring the position of an optically levitated nanoparticle at room temperature and without the overhead of an optical cavity. We use a fast heterodyne detection to reconstruct simultaneously orthogonal optical quadratures, and observe a noise reduction of $9\%\pm0.5\%$ below shot noise. Our experiment offers a nov…
Vacuum fluctuation, which is the intrinsic nature of an electric field can be measured via homodyne detection. Moreover, electric field intensity fluctuation are also related to vacuum fluctuations. Squeezed vacuum and sub-Poisson light can be obtained by controlling the vacuum fluctuation using noble nonlinear interaction. Based on the squeezed vacuum by inserting a mirror on the unused part of the beam splitter was proposed in 1994, we present the mode matching method for the vacuum and light fields. Light intensity fluctuations also can be reduced by inserting a mirror on the unused part of…
We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropic coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered: a three-dimensional cavity possessing eigenfrequencies $ω_3=3ω_1$, whose wall oscillates at the frequency $ω_w=2ω_1$, and a one-dimensional (Fabry--Perot) cavity with an equidistant spectrum $ω_n= nω_1$, when the distance between perfect mirrors oscillates at the f…
We propose two experimental schemes for producing coherent-state superpositions which approximate different nonclassical states conditionally in traveling optical fields. Although these setups are constructed of a small number of linear optical elements and homodyne measurements, they can be used to generate various photon number superpositions in which the number of constituent states can be higher than the number of measurements in the schemes. We determine numerically the parameters to achieve maximal fidelity of the preparation for a large variety of nonclassical states, such as amplitude …
