Matteo G. A. Paris
A high-sensitive interferometric scheme is presented. It is based on homodyne detection and squeezed vacuum phase properties. The resulting phase sensitivity scales as $δϕ\simeq {1/4} \bar{n}^{-1}$ with respect to input photons number.
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We theoretically investigate the phase sensitivity with parity detection on a Mach-Zehnder interferometer with a coherent state combined with a photon-added squeezed vacuum state. When the phase shift approaches zero, the squeezed vacuum state is indeed the optimal state within a constraint on the average number of photons. However, when the phase shift to be estimated slightly deviates from zero, the optimal state is neither the squeezed vacuum state nor the photon-subtracted squeezed vacuum state, but the photon-added squeezed vacuum state when they carry many photons. Finally, we show that …
The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.
We derive a general expression of the quantum Fisher information for a Mach-Zehnder interferometer, with the port inputs of an \emph{arbitrary} pure state and a squeezed thermal state. We find that the standard quantum limit can be beaten, when even or odd states are applied to the pure-state port. In particular, when the squeezed thermal state becomes a thermal state, all the even or odd states have the same quantum Fisher information for given photon numbers. For a squeezed thermal state, optimal even or odd states are needed to approach the Heisenberg limit. As examples, we consider several…
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…
A Mach-Zender interferometer with a gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase-interval. We obtain the optimal level of squeezing for a given phase-interval $Δθ_0$ and particle number $N$, with the resulting phase-estimation uncertainty smoothly approaching $3.5/N$ as $Δθ_0$ approaches 10/N, achieved with highly squeezed states near the Fock regime. We then analyze an adaptive measurement scheme which allows any phase on $(-π/2,π/2)$ to be measured with a precision of $3.5/N$ requiring only a few measurements, even for very la…
Strongly squeezed states of light are a key technology in boosting the sensitivity of interferometric setups, such as in gravitational-wave detectors. However, the practical use of squeezed states is limited by optical loss, which reduces the observable squeeze factor. Here we experimentally demonstrate that introducing squeezed states in additional, higher-order spatial modes can significantly improve the observed nonclassical sensitivity improvement when the loss is due to mode-matching deficiencies. Our results could be directly applied to gravitational-wave detectors, where this type of lo…
We present in this letter a scheme for optical interferometry. We utilize coherent-beam-stimulated two-mode squeezed light, which interacts with a phase shifter and is then squeezed again before detection. Our theoretical device has the potential to reach far below the shot noise limit (SNL) in phase sensitivity. This new proposal avoids the pitfalls of other setups, such as difficulty in creating the required resource. Furthermore, our scheme requires no complicated detection protocol, relying instead only on simple intensity measurement. Also, bright, coherent sources "boost" squeezed light,…
The fundamental quantum interferometry bound limits the sensitivity of an interferometer for a given total rate of photons and for a given decoherence rate inside the measurement device.We theoretically show that the recently reported quantum-noise limited sensitivity of the squeezed-light-enhanced gravitational-wave detector GEO600 is exceedingly close to this bound, given the present amount of optical loss. Furthermore, our result proves that the employed combination of a bright coherent state and a squeezed vacuum state is generally the optimum practical approach for phase estimation with h…
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
Storage and retrieval of a squeezed vacuum was successfully demonstrated using electromagnetically induced transparency. 930ns of the squeezed vacuum pulse was incident on the laser cooled 87Rb atoms with an intense control light in a coherent state. When the squeezed vacuum pulse was slowed and spatially compressed in the cold atoms, the control light was switched off. After 3us of storage, the control light was switched on again and the squeezed vacuum was retrieved, as was confirmed using the time-domain homodyne method.
Thermal activation of photon catalysis in difference-intensity Mach-Zehnder interferometry with squeezed thermal light
本文研究单模压缩热光作为初始资源的差强度马赫-曾德尔干涉仪，发现热激活的单光子催化可提升相位估计性能，差强度探测接近精度极限且鲁棒性良好。
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.
In this paper, we investigate the phase sensitivities in two-path optical interferometry with asymmetric beam splitters. Here, we present the optimal conditions for the transmission ratio and the phase of the beam splitter to gain the highest sensitivities for a general class of non-classical states with parity symmetry. Additionally, we address the controversial question of whether the scheme with a combination of coherent state and photon-added or photon-subtracted squeezed vacuum state is better or worse than the most celebrated one using a combination of coherent state and squeezed vacuum …
We show that the phase sensitivity $Δθ$ of a Mach-Zehnder interferometer fed by a coherent state in one input port and squeezed-vacuum in the other one is i) independent from the true value of the phase shift and ii) can reach the Heisenberg limit $Δθ\sim 1/N_T$, where $N_T$ is the average number of particles of the input states. We also show that the Cramer-Rao lower bound, $Δθ\propto 1/ \sqrt{|α|^2 e^{2r} + \sinh^2r}$, can be saturated for arbitrary values of the squeezing parameter $r$ and the amplitude of the coherent mode $|α|$ by a Bayesian phase inference protocol.
Bright squeezed vacuum, a macroscopic nonclassical state of light, can be obtained at the output of a strongly pumped non-seeded traveling-wave optical parametric amplifier (OPA). By constructing the OPA of two consecutive crystals separated by a large distance we make the squeezed vacuum spatially single-mode without a significant decrease in the brightness or squeezing.
The dissipative and decoherence properties as well as the asymptotic behavior of the single mode electromagnetic field interacting with the time-dependent squeezed vacuum field reservoir are investigated in detail by using the algebraic dynamical method. With the help of the left and right representations of the relevant $hw(4)$ algebra, the dynamical symmetry of the nonautonomous master equation of the system is found to be $su(1,1)$. The unique equilibrium steady solution is found to be the squeezed state and any initial state of the system is proved to approach the unique squeezed state asy…
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.
We have succeeded in observing ultraslow propagation of squeezed vacuum pulses with electromagnetically induced transparency. Squeezed vacuum pulses (probe lights) were incident on a laser cooled 87Rb gas together with an intense coherent light (control light). A homodyne method sensitive to the vacuum state was employed for detecting the probe pulse passing through the gas. A delay of 3.1us was observed for the probe pulse having a temporal width of 10 us.
In a strongly pumped non-degenerate traveling-wave OPA, we produce two-color squeezed vacuum with up to millions of photons per pulse. Our approach to registering this macroscopic quantum state is direct detection of a large number of transverse and longitudinal modes, which is achieved by making the detection time and area much larger than the coherence time and area, respectively. Using this approach, we obtain a record value of twin-beam squeezing for direct detection of bright squeezed vacuum. This makes direct detection of macroscopic squeezed vacuum a practical tool for quantum informati…
Finite-energy Gottesman-Kitaev-Preskill state-enhanced optical interferometry
本文分析有限能量GKP态增强的SU(2)和SU(1,1)干涉仪，证明宽包络GKP态在损耗下优于压缩真空，但低光子数时压缩真空更优，并给出QFI估计方法。
Enhancing the quantum entanglement and EPR steering of a coupled optomechanical system with a squeezed vacuum field
本文研究了在考虑机械模式引起的失谐位移时，利用弱压缩真空场增强耦合光机械系统的量子纠缠与EPR导引，发现参考相位比压缩参数起更关键的作用。
A probe light in a squeezed vacuum state was injected into cold 87 $Rb atoms with an intense control light in a coherent state. A sub-MHz window was created due to electromagnetically induced transparency, and the incident squeezed vacuum could pass through the cold atoms without optical loss, as was successfully monitored using a time-domain homodyne method.
There are two main approaches to generate the negative energy density (NED) in the literature. The Casimir effect and the squeezed vacuum. The possibility of the latter approach is qualitatively reviewed in this paper. It is proposed that the soliton theory may give remarkable contributions to generate and separate the NED out of the quantum vacuum. By applying the wavelength-division multiplexing (WDM) method on the solitonized laser beams which give rise the squeezed regions of the vacuum, it is shown the solitons' properties can be useful to the chosen approach.
Coherent electrons coupled to the quantized electromagnetic field undergo decoherence which can be viewed as due either to fluctuations of the Aharonov-Bohm phase or to photon emission. When the electromagnetic field is in a squeezed vacuum state, it is possible for this decoherence to be reduced, leading to the phenomenon of recoherence. This recoherence effect requires electrons which are emitted at selected times during the cycle of the excited mode of the electromagnetic field. We show that there are bounds on the degree of recoherence which are analogous to quantum inequality restriction …
Parity-detection-based Mach-Zehnder interferometry with coherent and non-Gaussian squeezed vacuum states as inputs
本文理论上研究了基于宇称探测的Mach-Zehnder干涉仪在相位估计中引入非高斯操作的优势，发现光子扣除、添加和催化均能提升相位灵敏度，其中单光子添加为最佳操作。
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 present an experimental realization of resonance fluorescence in squeezed vacuum. We strongly couple microwave-frequency squeezed light to a superconducting artificial atom and detect the resulting fluorescence with high resolution enabled by a broadband traveling-wave parametric amplifier. We investigate the fluorescence spectra in the weak and strong driving regimes, observing up to 3.1 dB of reduction of the fluorescence linewidth below the ordinary vacuum level and a dramatic dependence of the Mollow triplet spectrum on the relative phase of the driving and squeezed vacuum fields. Our r…
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 report on the generation of pulses of a low-frequency squeezed vacuum with noise suppression >2 dB below the standard quantum limit in a hot resonant 87 Rb vapor with polarization self-rotation. We demonstrate the possibility to precisely control the temporal profile of the squeezed noise quadrature by applying a calibrated longitudinal magnetic field, without degrading the maximum amount of squeezing.
A method for measuring the transmittivity of optical samples by using squeezed--vacuum radiation is illustrated. A squeezed vacuum field generated by a below--threshold optical parametric oscillator is propagated through a nondispersive medium and detected by a homodyne apparatus. The variance of the detected quadrature is used for measuring the transmittivity. With this method it is drastically reduced the number of photons passing through the sample during the measurement interval. The results of some tests are reported.
Enhancement of nonclassical properties of two-mode squeezed vacuum state with postselected von Neumann measurement
该研究探讨弱值放大对双模压缩真空态非经典特性的作用，并阐明基于该态的后选择弱测量优势。
Using the way of deriving infinitive sum representation of density operator as a solution to the master equation describing the amplitude dissipative channel by virtue of the entangled state representation, we show manifestly how the initial density operator of a single-mode squeezed vacuum state evolves into a definite mixed state which turns out to be a squeezed chaotic state with decreasing-squeezing. We investigate average photon number, photon statistics distributions for this state.
We propose a method to refine entanglement via swapping from a pair of squeezed vacuum states by performing the Bell measurement of number sum and phase difference. The resultant states are maximally entangled by adjusting the two squeezing parameters to the same value. We then describe the teleportation of number states by using the entangled states prepared in this way.
Squeezed vacuum field can be amplified or deamplified when it is injected, as the signal beam, into a phase-sensitive optical parametric amplifier (OPA) inside an optical cavity. The spectral features of the reflected quantized signal field are controlled by the relative phase between the injected squeezed vacuum field and the pump field for the OPA. The experimental results demonstrate coherent phenomena of OPA in the quantum regime, and show phase-sensitive manipulations of quantum fluctuations for quantum information processing.
A hybrid method of generating spin-squeezed states for quantum-enhanced atom interferometry
本文提出一种结合量子非破坏性测量和单轴扭曲的混合自旋压缩技术，在相互作用受限的实际情况下表现优于单独使用两种方法，且易于在现有原子干涉仪中实施。
We have developed a quantum memory technique that is completely compatible with current quantum information processing for continuous variables of light, where arbitrary frequency sidebands of a squeezed vacuum can be stored and retrieved using bichromatic electromagnetic induced transparency. 2MHz sidebands of squeezed vacuum pulses with temporal widths of 470ns and a squeezing level of -1.78 +- 0.02dB were stored for 3us in the laser-cooled 87Rb atoms. -0.44 +- 0.02dB of squeezing was retrieved, which is the highest squeezing ever reported for a retrieved pulse.
In this paper we experimentally study the statistical properties of a bright squeezed vacuum state containing up to 10^13 photons per mode (10 uJ per pulse), produced via high gain parametric down conversion (PDC). The effects of bunching and superbunching of photons were observed for a single mode PDC radiation by second-order intensity correlation function measurements with analog detectors.
Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.
In this paper, we theoretically investigate the displacement and momentum fluctuations spectra of the movable mirror in a standard optomechanical system driven by a finite bandwidth squeezed vacuum light accompanying a coherent laser field. Two cases in which the squeezed vacuum is generated by degenerated and non-degenerate parametric oscillators (DPO and NDPO) are considered. We find that for the case of finite bandwidth squeezed vacuum injection, the two spectra exhibit unique features, which strongly differ from those of broadband squeezing excitation. In particular, the spectra exhibit a …
We experimentally and theoretically analyze the transmission of continuous-wave and pulsed squeezed vacuum through rubidium vapor under the conditions of electromagnetically induced transparency. Frequency- and time-domain homodyne tomography is used to measure the quadrature noise and reconstruct the quantum states of the transmitted light. A simple theoretical model explains the spectrum and degradation of the transmitted squeezing with high precision.
A non-dichotomic Bell-type inequality for macroscopic photon numbers in two spatially separated beams is derived from local realistic assumptions. This inequality is shown to be possible to violate with the macroscopic Bell states recently obtained in experiment.
Decay parameter of coherence and population inversion are calculated from the master equation of a two level atom tunneling through a squeezed vacuum. Using those parameters, the timescales for decoherence and zeno effect are calculated in the weak measurement scheme. By comparing those timescales, a certain condition has been found for sustainable coherent dynamics.
Tunneling of a two-state particle through a squeezed vacuum is considered. It has been shown that repetitive measurement or interaction with the external field can preserve the coherence. Moreover, the coherence time in terms of the squeezing parameters has been calculated. A specific condition is derived, under which the coherence is sustainable.
We report a 65MHz-bandwidth triangular-shaped optical parametric oscillator (OPO) for squeezed vacuum generation at 860nm. The triangle structure of our OPO enables the round-trip length to reach 45mm as a ring cavity, which provides a counter circulating optical path available for introducing a probe beam or generating another squeezed vacuum. Hence our OPO is suitable for the applications in high-speed quantum information processing where two or more squeezed vacua form a complicated interferometer, like continuous-variable quantum teleportation. With a homemade, broadband and low-loss homod…
We report generation of a continuous-wave squeezed vacuum resonant on the Rb D_1 line (795 nm) using periodically poled KTiOPO_4 (PPKTP) crystals. With a frequency doubler and an optical parametric oscillator based on PPKTP crystals, we observed a squeezing level of -2.75 +- 0.14 dB and an anti-squeezing level of +7.00 +- 0.13 dB. This system could be utilized for demonstrating storage and retrieval of the squeezed vacuum, which is important for the ultra-precise measurement of atomic spins as well as quantum information processing.
Direct photon detection is experimentally implemented to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. Following a recent theoretical proposal [arXiv quant-ph/0311119], the setup only requires a tunable beamsplitter and a single-photon detector to fully characterize the generated Gaussian states. The experimental implementation of this procedure is discussed and compared with other reference methods.
We show, by making conditional measurements on the Einstein-Podolsky-Rosen (EPR) squeezed vacuum, that one can improve the efficacy of teleportation for both the position difference, momentum sum and number difference, phase sum continuous variable teleportation protocols. We investigate the relative abilities of the standard and conditional EPR states, and show that by conditioning we can improve the fidelity of teleportation of coherent states from below to above the $\bar{F} = 2/3$ boundary.
In this work, we introduce a non-Gaussian quantum state named excited squeezed vacuum state (ESVS), which can be ustilized to describe quantum light field emitted from the multiphoton quantum process occurred in some restricted quantum systems. We investigate its nonclassical properties such as Wigner distribution in phase space, photon number distribution, the second-order autocorrelation and the quadrature fluctuations. By virtue of the Hilbert-Schmidt distance method, we quantify the non-Gaussianity of the ESVS. Due to the similar photon statistics, we examine the fidelity between the ESVS …
Classical Model for Broadband Squeezed Vacuum Driving Two-Photon Absorption or Sum Frequency Generation
本文提出经典随机场模型，通过真空能项扣除（重整化）方法，在宽带压缩真空驱动的双光子吸收和和频产生中，于低增益和高增益机制下均给出与完整量子场论完全相同的预测。
We demonstrate the simultaneous quantum state reconstruction of the spectral modes of the light field emitted by a continuous wave degenerate optical parametric amplifier. The scheme is based on broadband measurement of the quantum fluctuations of the electric field quadratures and subsequent Fourier decomposition into spectral intervals. Applying the standard reconstruction algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of density matrices and Wigner functions is obtained. The recorded states show a smooth transition from the squeezed vacuum to a vacuum state. In the ti…
Theoretical analysis is given for a two-photon subtraction from a continuous wave (CW) squeezed vacuum with finite time separation between two detection events. In the CW photon subtraction process, the generated states are inevitably described by temporal mutimode states. Our approach is based on Schrödinger picture which provides mathematically simple forms and an intuitive understanding of its multimode structure. We show that, in our process, the photon subtracted squeezed vacuum is generated in two temporal modes and one of these modes acts as an ancillary mode to make the other one a lar…
Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all the macroscopic Bell states, containing typically $10^6$ photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations.
Adding or Subtracting a single Photon is the same for Pure Squeezed Vacuum States
该研究证明纯压缩真空态在添加或减去单个光子时结果相同，并指出混合态在特定条件下也具备此特性。
Applying stochastic differential equations, we study the squeezing and statistical properties of the cavity and output modes of a degenerate three-level laser whose cavity contains a parametric amplifier and coupled to a squeezed vacuum reservoir. We consider the case in which the top and bottom levels of the three-level cascade atoms injected into the cavity are coupled by the pump mode emerging from the parametric amplifier. It turns out that the presence of the squeezed vacuum reservoir and the parametric amplifier contribute considerably to the mean photon number and the degree of squeezin…
Squeezed states of harmonic oscillators are a central resource for continuous-variable quantum sensing, computation and communication. Here we propose a method for the generation of very good approximations to highly squeezed vacuum states with low excess anti-squeezing using only a few oscillator-qubit coupling gates through a Rabi-type interaction Hamiltonian. This interaction can be implemented with several different methods, which has previously been demonstrated in superconducting circuit and trapped-ion platforms. The protocol is compatible with other protocols manipulating quantum harmo…
We optimize the signal-to-noise ratio of a Mach-Zehnder atom interferometer with Gaussian squeezed input states, in the presence interactions. For weak interactions, our results coincide with Phys. Rev. Lett. {\bf 100}, 250406 (2008), with optimal initial number-variance $σ_o\propto N^{1/3}$ and optimal signal-to-noise ratio $s_o\propto N^{2/3}$ for total atom number $N$. As the interaction strength $u$ increases past unity, phase-diffusion becomes dominant, leading to a transition in the optimal squeezing from initial number-squeezing to initial {\it phase}-squeezing with $σ_o\propto\sqrt{uN}…
Employing the master equation for a three-level laser driven by coherent light and coupled to a squeezed vacuum reservoir, we obtain stochastic differential equations associated with the normal ordering. Using the solutions of the stochastic differential equations, we calculate the quadrature variance, the squeezing spectrum, the mean photon number, and the variance of the photon number. It turns out that the degree of squeezing increases with the linear gain coefficient or the squeeze parameter. It is also found that the driving coherent light decreases the mean photon number.
We study the sensitivity and resolution of phase measurement in a Mach-Zehnder interferometer with two-mode squeezed vacuum (<n> photons on average). We show that super-resolution and sub-Heisenberg sensitivity is obtained with parity detection. In particular, in our setup, dependence of the signal on the phase evolves <n> times faster than in traditional schemes, and uncertainty in the phase estimation is better than 1/<n>.
Using a traveling-wave OPA with two orthogonally oriented type-I BBO crystals pumped by picosecond pulses, we generate vertically and horizontally polarized squeezed vacuum states within a broad range of wavelengths and angles. Depending on the phase between these states, fluctuations in one or another Stokes parameters are suppressed below the shot-noise limit. Due to the large number of photon pairs produced, no local oscillator is required, and 3dB squeezing is observed by means of direct detection.
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…
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