We present an entanglement criterion for two mode squeezed states which relies on particle counting only. The proposed inequality is optimal for the state under consideration and robust against particle losses up to 2/3. As it does not involve measurements of quadratures - which is typically very challenging for atomic modes - it renders the detection of atomic many-particle entanglement feasible in many different settings. Moreover it bridges the gap between entanglement verification for a qubit and criteria for continuous variables measured by homodyne detection. We illustrate its application in the context of superradiant light scattering from Bose Einstein condensates by considering the creation of entanglement between atoms and light as well as between two condensates in different momentum states. The latter scheme takes advantage of leaving the Gaussian realm and features probabilistic entanglement distillation.
We measure the population distribution in one of the atomic twin beams generated by four-wave mixing in an optical lattice. Although the produced two-mode squeezed vacuum state is pure, each individual mode is described as a statistical mixture. We confirm the prediction that the particle number follows an exponential distribution when only one spatio-temporal mode is selected. We also show that this distribution accounts well for the contrast of an atomic Hong--Ou--Mandel experiment. These experiments constitute an important validation of our twin beam source in view of a future test of a Bel…
We discuss the possibilities of studying in detail the dynamics of spontaneous emission of a single photon by a single atom and measuring the transient degree of squeezing by means of full solid angle fluorescence detection.
Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [1]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, -1.2 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these m…
Recently, a non-Gaussian state, which is called cubic phase state has been experimentally realized. In this work we show that, in case one has access to a proper cubic phase state, it is possible to make photon counting experiments and generate extremely squeezed states.
A general formalism for computing the full counting statistics of energy exchanged between 'N' squeezed thermal photon reservoirs weakly coupled to a cavity with 'M' photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases, the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time statistics is signifi…
We suggest a scheme of using two-mode squeezed vacuum for conditional teleportation of quantum states of optical field. Alice mixes the input state with one of the squeezed modes on another squeezing device and detects the output photon numbers. The result is then communicated to Bob who shifts the photon number of his part accordingly. This is a principally realizable modification of the recent scheme [G.J. Milburn and S.L. Braunstein, Phys. Rev. A 60, 937 (1999)] where measurements of photon number difference and phase sum are considered. We show that for some classes of states this method c…
Two-photon absorption (TPA) is of fundamental importance in super-resolution imaging and spectroscopy. Its nonlinear character allows for the prospect of using quantum resources, such as entanglement, to improve measurement precision or to gain new information on, e.g., ultrafast molecular dynamics. Here, we establish the metrological properties of nonclassical squeezed light sources for precision measurements of TPA cross sections. We find that there is no fundamental limit for the precision achievable with squeezed states in the limit of very small cross sections. Considering the most releva…
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so called `dark port case', when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (`dark port'). For this case it had been suggested that signal amplification is possible without concurrent noise a…
Squeezed states of light reduce the signal-normalized photon counting noise of measurements without increasing the light power and enable fundamental research on quantum entanglement in hybrid systems of light and matter. Furthermore, the completion of squeezed states with cryo-cooling has high potential. First, measurement sensitivities are usually limited by quantum noise and thermal noise. Second, squeezed states allow for reducing the heat load on cooled devices without losing measurement precision. Here, we demonstrate squeezed-light position sensing of a cryo-cooled micro-mechanical memb…
Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a specially designed quantum state. The success of such a scheme usually relies on the process belonging to a particular one-parameter family. If this assumption is violated, or if the goal is to measure more than one parameter, a different quantum state may perform better. In the most extreme case, we know nothing about the process and wish to learn everything.…
We realize and test in experiment a method recently proposed for measuring absolute quantum efficiency of analog photodetectors. Similarly to the traditional (Klyshko) method of absolute calibration, the new one is based on the direct detection of two-mode squeezed vacuum at the output of a traveling wave OPA. However, in the new method one measures the difference-photocurrent variance rather than the correlation function of photocurrents (number of coincidences), which makes the technique applicable for high-gain OPA. In this work we test the new method versus the traditional one for the case…
A cavity QED system is analyzed which duplicates the dynamics of a two-level atom in free space interacting exclusively with broadband squeezed light. We consider atoms in a three or four-level Lambda-configuration coupled to a high-finesse optical cavity which is driven by a squeezed light field. Raman transitions are induced between a pair of stable atomic ground states via the squeezed cavity mode and coherent driving fields. An analysis of the reduced master equation for the atomic ground states shows that a three-level atomic system has insufficient parameter flexibility to act as an effe…
The detection and characterization of a non-classical-squeezed state of light, by using two different schemes, will be presented . In the first one, in an one-dimensional cavity with moving mirror (non-stationary Casimir effect) in the principal mode, we study the photon creation rate for two modes (squeezed and coherent state) of driving field. Since the cavity with moving mirror (similar to an optomechanical system) can be considered analogue to a Kerr-like medium, so that in the second scheme, the probability amplitude for multi-photons absorption in a nonlinear (Kerr) medium will be quantu…
We study in detail a system of two interferometers aimed to the detection of extremely faint phase-fluctuations. This system can represent a breakthrough for detecting a faint correlated signal that would remain otherwise undetectable even using the most sensitive individual interferometric devices, that are limited by the shot noise. If the two interferometers experience identical phase-fluctuations, like the ones introduced by the so called "holographic noise", this signal should emerge if their output signals are correlated, while the fluctuations due to shot noise and other independent con…
We explore the effects of quantum mechanical squeezing on the nonequilibrium fluctuations of bosonic transport between two squeezed harmonic reservoirs and a two level system. A standard full counting statistics technique based on a quantum master equation is employed. We derive a nonzero thermodynamic affinity under equal temperature setting of the two squeezed reservoirs. The odd cumulants are shown to be independent of squeezing under symmetric conditions, whereas the even cumulants depend nonlinearly on the squeezing parameters. The odd and even cumulants saturate at two different but uniq…
We explore the possibility of entanglement detection in continuous variable systems by entanglement witnesses based on covariance matrices, constructible from random homodyne measurements. We propose new linear constraints characterizing the entanglement witnesses based on second moments, and use them in a semidefinite program providing the optimal entanglement test for given random measurements. We test the method on the class of squeezed vacuum states and study the efficiency of entanglement detection in general unknown covariance matrices.
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cyc…
The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a `nulling' measurement (squeezing and photon counting) to achiev…
This paper reviews quantum spin squeezing, which characterizes the sensitivity of a state with respect to an SU(2) rotation, and is significant for both entanglement detection and high-precision metrology. We first present various definitions of spin squeezing parameters, explain their origin and properties for typical states, and then discuss spin-squeezed states produced with the Ising and the nonlinear twisting Hamiltonians. Afterwards, we explain correlations and entanglement in spin-squeezed states, as well as the relations between spin squeezing and quantum Fisher information, where the …
In this paper we describe that the optically pumped frequency standards can have frequency stability beyond the quantum noise limit by detecting the Ramsey resonance through the squeezed light. In this paper we report that instead of considering the interaction of entangled atoms in the microwave region, it will be more practical to create the entanglement of the atoms in the detection region using the squeezed light, which is also used for the detection of the Ramsey resonance. The advantage of squeezing can be derived when the technical noises have been removed.
We present a method of directly obtaining the parity of a Gaussian state of light without recourse to photon-number counting. The scheme uses only a simple balanced homodyne technique, and intensity correlation. Thus interferometric schemes utilizing coherent or squeezed light, and parity detection may be practically implemented for an arbitrary photon flux. Specifically we investigate a two-mode, squeezed-light, Mach-Zehnder interferometer and show how the parity of the output state may be obtained. We also show that the detection may be described independent of the parity operator, and that …
We show how the presence of entanglement in a bipartite Gaussian state can be detected by the amount of work extracted by a continuos variable Szilard-like device, where the bipartite state serves as the working medium of the engine. We provide an expression for the work extracted in such a process and specialize it to the case of Gaussian states. The extractable work provides a sufficient condition to witness entanglement in generic two-mode states, becoming also necessary for squeezed thermal states. We extend the protocol to tripartite Gaussian states, and show that the full structure of in…
Loophole-free Bell tests are essential if one wishes to perform device-independent quantum key distribution (QKD), since any loophole could be used by a potential adversary to undermine the security of the protocol. Crucial work by Eberhard demonstrated that weakly entangled two-qubit states have a far greater resistance to the detection loophole than maximally entangled states, allowing one to close the loophole with detection efficiency greater than 2/3. Here we demonstrate that this same limit holds for photon-counting CHSH Bell tests which can demonstrate non-locality for higher dimensiona…
This study focuses on generating and manipulating squeezed states with two external oscillators coupled by an InP HEMT transistor operating at cryogenic temperatures. First, the small-signal nonlinear model of the transistor at high frequency at 5 K is analyzed using quantum theory, and the related Lagrangian is theoretically derived. Subsequently, the total quantum Hamiltonian of the system is derived using Legendre transformation. The Hamiltonian of the system includes linear and nonlinear terms, by which the effects on the time evolution of the states are studied. The main result shows that…
We consider improving the sensitivity of future interferometric gravitational-wave detectors by simultaneously injecting two squeezed vacuums (light), filtered through a resonant Fabry-Perot cavity, into the dark port of the interferometer.The same scheme with single squeezed vacuum was first proposed and analyzed by Corbitt et al. Here we show that the extra squeezed vacuum, together with an additional homodyne detection suggested previously by one of the authors, allows reduction of quantum noise over the entire detection band. To motivate future implementations, we take into account a reali…
Non-existence of a local hidden variables (LHV) model for a phenomenon benchmarks its use in device-independent quantum protocols. Nowadays photon-number resolving weak-field homodyne measurements allow realization of emblematic gedanken experiments. Alas, claims that we can have no LHV models for such experiments on (a) excitation of a pair of spatial modes by a single photon, and (b) two spatial modes in a weakly squeezed vacuum state, involving constant local oscillator strengths, are unfounded. For (a) an exact LHV model resolves the dispute on the "non-locality of a single photon" in its …
We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are function of the internal phase-shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuum at the input leads to maximum entangled state at the output. The fringes visibilities resulting from measuring the coincidence counting rat…
We introduce a method for efficient, in situ characterization of linear-optical networks (LONs) in randomized boson-sampling (RBS) experiments. We formulate RBS as a distributed task between two parties, Alice and Bob, who share two-mode squeezed-vacuum states. In this protocol, Alice performs local measurements on her modes, either photon counting or heterodyne. Bob implements and applies to his modes the LON requested by Alice; at the output of the LON, Bob performs photon counting, the results of which he sends to Alice via classical channels. In the ideal situation, when Alice does photon …
We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. The stochastic master equation or stochastic Schrödinger equation describing the measurement process includes both jump-type and diffusive-type stochastic increments. Analytic expressions of the wave function conditioned on homodyne and photon-counting records are obtained, yielding the probability density distributions and generating functions of the measurement records. Formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived which quantitativel…
Photon antibunching is a quantum phenomenon typically observed in strongly nonlinear systems where photon blockade suppresses the probability for detecting two photons at the same time. Antibunching has also been reported with Gaussian states, where optimized amplitude squeezing yields classically forbidden values of the intensity correlation, $g^{(2)}(0)<1$. As a consequence, observing antibunching is not necessarily a signature of photon-photon interactions. To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing if a field is non-Gaussian bas…
Enhancing quantum entanglement is important for many quantum information processing applications. In this paper, we consider a protocol for entanglement enhancing in a two-mode squeezed vacuum state (TMSVS), attained based on photon subtraction, photon catalysis, and photon addition. Central to such an operation is the task of mixing and detecting number states with each mode of TMSVS. We analyze various settings and find an optimal setup for improving the entanglement of the state.
We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle's wavefunction toward a narrow Gaussian wavepacket at the location $x_\mathrm{est}$ determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle's position, as calculated from the post-measurement wavefunction agrees precisely with shot-noise limited uncertainty of th…
The final goal of quantum hypothesis testing is to achieve quantum advantage over all possible classical strategies. In the protocol of quantum reading this advantage is achieved for information retrieval from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. For this protocol, we show, theoretically and experimentally, that quantum advantage is obtained by practical photon-counting measurements combined with a simple maximum-likelihood decision. In particular, we show that this receiver combined with an entangled two-mode squeezed vacuum source …
The protocol of quantum reading refers to the quantum enhanced retrieval of information from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. In the following we analyze the case of a particular class of optical receiver, based on photon counting measurement, since they can be particularly simple in view of real applications. We show that a quantum advantage is achievable when a transmitter based on two-mode squeezed vacuum (TMSV) states is combined with a photon counting receiver, and we experimentally confirm it. In this paper, after introduci…
Classical versus non-classical photon states for detecting vacuum non-linearity
Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿罗森多夫赫尔姆霍兹中心）；The Extreme Light Infrastructure ERIC, ELI Beamlines Facility（极端光基础设施欧洲研究联盟，ELI光束线设施）；Institut für Theoretische Physik, Technische Universität Dresden（德累斯顿工业大学理论物理研究所）
During the theoretical investigation of the ultimate sensitivity of gravitational wave detectors through the 1970's and '80's, it was debated whether quantum fluctuations of the light field used for detection, also known as photon shot noise, would ultimately produce a force noise which would disturb the detector and limit the sensitivity. Carlton Caves famously answered this question with "They do." With this understanding came ideas how to avoid this limitation by giving up complete knowledge of the detector's motion. In these back-action evading (BAE) or quantum non-demolition (QND) schemes…
Detecting traveling photons is an essential primitive for many quantum information processing tasks. We introduce a single-photon detector design operating in the microwave domain, based on a weakly nonlinear metamaterial where the nonlinearity is provided by a large number of Josephson junctions. The combination of weak nonlinearity and large spatial extent circumvents well-known obstacles limiting approaches based on a localized Kerr medium. Using numerical many-body simulations we show that the single-photon detection fidelity increases with the length of the metamaterial to approach one at…
The problem of long-distance teleportation of single-atom qubits via a common photonic channel is examined within the framework of a Mach-Zender optical interferometer. As expected, when a coherent state is used as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. However, we find that a number-squeezed light field in a twin-Fock state can in principle create useful entanglement without cavity-enhancement. Both approaches require single photon counting detectors, and best results are obtained by combining cavity-feedback with twin-fock inputs. Su…
Entanglement entropy is a measure of quantum correlations between separate parts of a many-body system, which plays an important role in many areas of physics. Here we review recent work in which a relation between this quantity and the Full Counting Statistics description of electron transport was established for noninteracting fermion systems. Using this relation, which is of a completely general character, we discuss how the entanglement entropy can be directly measured by detecting current fluctuations in a driven quantum system such as a quantum point contact.
We propose a scheme based on using the singlet ground state of an electron spin pair in a double quantum dot nanostructure as a suitable set-up for detecting entanglement between electron spins via the measurement of an optimal entanglement witness. Using time-dependent gate voltages and magnetic fields the entangled spins are separated and coherently rotated in the quantum dots and subsequently detected at spin-polarized quantum point contacts. We analyze the coherent time evolution of the entangled pair and show that by counting coincidences in the four exits an entanglement test can be done…
We propose a realistic device for detecting objects almost without transferring a single quantum of energy to them. The device can work with an efficiency close to 100% and relies on two detectors counting both presence and absence of the objects. Its possible usage in performing fundamental experiments as well as possible applications are discussed.
The Michelson interferometer is a cornerstone of experimental physics. Its applications range from providing first impressions of wave interference in educational settings to probing spacetime at minuscule precision scales. Interferometer precision provides a unique view of the fundamental medium of matter and energy, enabling tests for new physics as well as searches for the gravitational wave signatures of distant astrophysical events. Optical interferometers are typically operated by continuously measuring the power at their output port. Signal perturbations then create sideband fields, for…
The Kitaev surface-code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the disti…
Quantum illumination is a technique for detecting the presence of a target in a noisy environment by means of a quantum probe. We prove that the two-mode squeezed vacuum state is the optimal probe for quantum illumination in the scenario of asymmetric discrimination, where the goal is to minimize the decay rate of the probability of a false positive with a given probability of a false negative. Quantum illumination with two-mode squeezed vacuum states offers a 6 dB advantage in the error probability exponent compared to illumination with coherent states. Whether more advanced quantum illuminat…
We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore we have a refined bound for…
