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 $ g^{(2)} $ factor of the generated light inside the cavity in the steady state.
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 …
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.
Continuous-variable (CV) entanglement is a valuable resource in the field of quantum information. One source of CV entanglement is the correlations between the position and momentum of photons in a two-mode squeezed state of light. In this paper, we theoretically study the generation of squeezed states, via spontaneous parametric downconversion (SPDC), inside a two-mode lossy cavity that is pumped with a classical optical pulse. The dynamics of the density operator in the cavity is modelled using the Lindblad master equation, and we show that the exact solution to this model is the density ope…
We study the precise phase estimation using squeezed states with photon losses present. Our exact quantum Fisher information calculation shows significant quantum enhancement and thus reveals the benchmark for practical quantum metrology in this noisy scenario. However, we find that the existing parity measurement scheme [P.M. Anisimov et al, Phys. Rev. Lett. 104, 103602 (2010)] behaves worse than even classical cases given very small losses, unless we take an appropriate loss dependent phase shift. Using our formulae, the two optimized aspects including the pre-detection phase shift and the c…
The interaction between quantum light and matter is being intensively studied for systems that are enclosed in high-$Q$ cavities which strongly enhance the light-matter coupling. However, for many applications, cavities with lower $Q$-factors are preferred due to the increased spectral width of the cavity mode. Here, we investigate the interaction between quantum light and matter represented by a $Λ$-type three-level system in lossy cavities, assuming that cavity losses are the dominant loss mechanism. We demonstrate that cavity losses lead to non-trivial steady states of the electronic occupa…
We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum …
In this work we examine the entanglement of the output signal-idler squeezed vacuum state in the Heisenberg picture as a function of the coupling and internal propagation loss parameters of a microring resonator. Using the log-negativity as a measure of entanglement for a mixed Gaussian state, we examine the competitive effects of the transfer matrix that encodes the classical phenomenological loss, as well as the matrix that that incorporates the coupling and internal propagation loss due to the quantum Langevin noise fields required to preserve unitarity of the composite system,(signal-idler…
The quantum Fisher information for a two-mode, Gaussian product state in an interferometer subject to photon loss is studied. We obtain the quantum Cramer-Rao bound on the achievable precision in phase estimation using such states. The scaling of the measurement precision with the mean photon number for such input product states is compared to the limited scaling for dual squeezed vacuum states and for dual squeezed, displaced vacuum states.
We study the phase sensitivity in the conventional $SU(2)$ and nonconventional $SU(1,1)$ interferometers with the coherent and squeezed vacuum input state via the quantum Cramer-Rao bound. We explicitly construct the detection scheme that gives the optimal phase sensitivity. For practical purposes, we show that in the presence of photon loss, both interferometers with proper homodyne detections, are nearly optimal. We also find that unlike the coherent state and squeezed vacuum state, the effects of the imperfect detector on the phase sensitivity cannot be asymptotically removed for a generic …
We present a new derivation of the Casimir force between two parallel plane mirrors at zero temperature. The two mirrors and the cavity they enclose are treated as quantum optical networks. They are in general lossy and characterized by frequency dependent reflection amplitudes. The additional fluctuations accompanying losses are deduced from expressions of the optical theorem. A general proof is given for the theorem relating the spectral density inside the cavity to the reflection amplitudes seen by the inner fields. This density determines the vacuum radiation pressure and, therefore, the C…
This paper focuses on changing Fock matrix elements of two-mode squeezed vacuum state (TMSVS) by employing three quantum operations in one-sided lossy channel. These three quantum operations include one-photon replacement (OPR), one-photon substraction (OPS) and one-photon addition (OPA). Indeed, three conditional quantum states have been generated from the original TMSVS. Using the characteristic function (CF) representation of quantum density operator, we derive the analytical expressions of their Fock matrix elements, which are dependent on the interaction parameters, including the squeezin…
The ultimate limits of continuous-variable single-mode quantum teleportation due to absorption are studied, with special emphasis on (quasi-)monochromatic optical fields propagating through fibers. It is shown that even if an infinitely squeezed two-mode squeezed vacuum were used, the amount of information that would be transferred quantum mechanically over a finite distance is limited and effectively approaches to zero on a length scale that is much shorter than the (classical) absorption length. Only for short distances the state-dependent teleportation fidelity can be close to unity. To rea…
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.
Position-Resolved Resonance Quantization for Lossy Cavities
Albert-Ludwigs-Universität Freiburg（弗赖堡大学）；EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg（阿尔伯特-路德维希-弗赖堡大学 EUCOR 量子科学与量子计算中心）
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…
Transfer of nonlocal two-mode squeezed vacuum state through symmetrical and asymmetrical lossy channel is analysed and we demonstrate that the nonlocality is more robust against losses, than it has been previously suggested. It can be important for security of continuous-variable quantum cryptography employing entangled states.
Within the framework of exact quantization of the electromagnetic field in dispersing and absorbing media the input-output problem of a high-$Q$ cavity is studied, with special emphasis on the absorption losses in the coupling mirror. As expected, the cavity modes are found to obey quantum Langevin equations, which could be also obtained from quantum noise theories, by appropriately coupling the cavity modes to dissipative systems, including the effect of the mirror-assisted absorption losses. On the contrary, the operator input-output relations obtained in this way would be incomplete in gene…
The paper continues the analysis of vacuum Rabi oscillations we started in Part I [Phys. Rev. A {\bf 79}, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic oscillator Lie algebras. The zero-temperature master equation, derived in Part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic fields by a gas of harmonic oscillator wave packets. The representation is known to introduce automatic regularizations that in irreducible representations…
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…
The 1996 Brune {\it et al.} experiment on vacuum Rabi oscillation is analyzed by means of alternative models of atom-reservoir interaction. Agreement with experimental Rabi oscillation data can be obtained if one defines jump operators in the dressed-state basis, and takes into account thermal fluctuations between dressed states belonging to the same manifold. Such low-frequency transitions could be ignored in a closed cavity, but the cavity employed in the experiment was open, which justifies our assumption. The cavity quality factor corresponding to the data is $Q=3.31\cdot 10^{10}$, whereas…
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…
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.
Dynamics of entangled states of two independent single-mode cavities in squeezed reservoirs is investigated in the context of matching of the correlations contained in the entangled states to those contained in the squeezed reservoir. We illustrate our considerations by examining the time evolution of entanglement of single and double excitation NOON and EPR states. A comparison is made when each cavity is coupled to own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservo…
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.
We show that, under certain circumstances, an optical field in a two-mode squeezed vacuum (TMSV) state can propagate through a lossy atomic medium without degradation or evolution. Moreover, the losses give rise to that state when a different state is initially injected into the medium. Such a situation emerges in a Λ-type atomic system, in which both optical transitions are driven by strong laser fields that are two-photon resonant with the respective signal modes. Then the interactions of the two signal modes with the ground-state atomic coherence interfere destructively, thereby ensuring th…
Squeezed light has evolved into a powerful tool for quantum technology, ranging from quantum enhanced sensing and quantum state engineering based on partial post-selection techniques. The pulsed generation of squeezed light is of particular interest, as it can provide accurate time stamp and physically defined temporal mode, which are highly preferred in complex communication networks and large-scale information processing. However, the multimode feature of pulsed squeezing in conventional single-pass configuration limits the purity of the output state, negatively impacting its application in …
We present an integrated source of counterpropagating entangled states based on a coupled resonator optical waveguide that is pumped by a classical pulsed source incident from above the waveguide. We investigate theoretically the generation and propagation of continuous variable entangled states in this coupled-cavity system in the presence of intrinsic loss. Using a tight-binding approximation, we derive analytic time-dependent expressions for the number of photons in each cavity, as well as for the correlation variance between the photons in different pairs of cavities, to evaluate the degre…
Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the lossy parameter, we study the energy-constrained quantum Fisher information (QFI) for generic temperature and lossy parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum…
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…
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 study the problem of estimating the Schwarzschild radius of a massive body using Gaussian quantum probe states. Previous calculations assumed that the probe state remained pure after propagating a large distance. In a realistic scenario, there would be inevitable losses. Here we introduce a practical approach to calculate the Quantum Fisher Informations (QFIs) for a quantum probe that has passed through a lossy channel. Whilst for many situations loss means coherent states are optimal, we identify certain situations for which squeezed states have an advantage. We also study the effect of th…
The ongoing global effort to detect gravitational waves continues to push the limits of precision measurement while aiming to provide a new tool for understanding both astrophysics and fundamental physics. Squeezed states of light offer a proven means of increasing the sensitivity of gravitational wave detectors, potentially increasing the rate at which astrophysical sources are detected by more than an order of magnitude. Since radiation pressure noise plays an important role in advanced detectors, frequency dependent squeezing will be required. In this paper we propose a practical approach t…
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 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.
The exact reduced dynamics for the independent oscillator model in the RWA approximation at zero and finite temperatures is derived. It is shown that the information about the interaction and the environment is encapsulated into three time dependent coefficients of the master equation, one of which vanishes in the zero temperature case. In currently used optical cavities all the information about the field dynamics is contained into {\it two} (or three) experimentally accesible and physically meaningful real functions of time. From the phenomenological point of view it suffices then to careful…
We propose an alternative scheme for nonreciprocal light propagation in two coupled cavities system, in which a two-level quantum emitter is coupled to one of the optical microcavities. For the case of parity-time (\textrm{PT}) system (i.e., active-passive coupled cavities system), the cavity gain can significantly enhance the optical nonlinearity induced by the interaction between a quantum emitter and cavity field beyond weak-excitation approximation. The giant optical nonlinearity results in the non-lossy nonreciprocal light propagation with high isolation ratio in proper parameters range. …
Bosonic channels describe quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We investigate the maximum rates for the bosonic multiple access channel (MAC) in the presence of thermal noise added by the environment and when the transmitters utilize Gaussian state inputs. We develop an outer bound for the capacity region for the thermal-noise lossy bosonic MAC. We additionally find that the use of coherent states at the transmitters is capacity-achieving in the limits of high and low mean input photon numbers. Furthermore, we verify that coher…
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 an experiment to extract ponderomotive squeezing from an interferometer with high circulating power and low mass mirrors. In this interferometer, optical resonances of the arm cavities are detuned from the laser frequency, creating a mechanical rigidity that dramatically suppresses displacement noise. After taking into account imperfection of optical elements, laser noise, and other technical noise consistent with existing laser and optical technologies and typical laboratory environments, we expect the output light from the interferometer to have measurable squeezing of ~5 dB, with…
In this work we analyse the structure of highly-entangled multimode squeezed states, such as those generated by broadband pulses undergoing type-II parametric down-conversion (PDC). Such down-conversion has previously been touted as a natural and efficient means of cluster-state generation, and therefore a viable future pathway to quantum computation. We first detail how broadband PDC processes lead directly to a series of orthogonal supermodes that are linear combinations of the original frequency modes. We then calculate the total squeezing of the multimode entangled states when they are ass…
The strong light-matter coupling attainable in optical cavities enables the generation of highly squeezed states of atomic ensembles. It was shown in [Phys. Rev. A 66, 022314 (2002)] how an effective one-axis twisting Hamiltonian can be realized in a cavity setup. Here, we extend this work and show how an effective two-axis twisting Hamiltonian can be realized in a similar cavity setup. We compare the two schemes in order to characterize their advantages. In the absence of decoherence, the two-axis Hamiltonian leads to more squeezing than the one-axis Hamiltonian. If limited by decoherence fro…
We consider the discrimination of lossy bosonic channels and focus to the case when one of the values for the loss parameter is zero, i.e., we address the detection of a possible loss against the alternative hypothesis of an ideal lossless channel. This discrimination is performed by inputting one-mode or two-mode squeezed thermal states with fixed total energy. By optimizing over this class of states, we find that the optimal inputs are pure, thus corresponding to single- and two-mode squeezed vacuum states. In particular, we show that for any value of the damping rate smaller than a critical…
Twin-Signal-Recycling (TSR) builds on the resonance doublet of two optically coupled cavities and efficiently enhances the sensitivity of an interferometer at a dedicated signal frequency. We report on the first experimental realization of a Twin-Signal-Recycling Michelson interferometer and also its broadband enhancement by squeezed light injection. The complete setup was stably locked and a broadband quantum noise reduction of the interferometers shot noise by a factor of up to 4\,dB was demonstrated. The system was characterized by measuring its quantum noise spectra for several tunings of …
