Squeezed Vacuum Input Research Articles

Heisenberg-limited estimation robust to photon losses in a Mach-Zehnder network with squeezed light

We propose a multi-parameter quantum metrological protocol based on a Mach-Zehnder interferometer with a squeezed vacuum input state and an anti-squeezing operation at one of its output channels. A simple and intuitive geometrical picture of the state evolution is provided by the marginal Wigner functions of the state at each interferometer output channel. The protocol allows to detect the value of the sum $\beta=\frac{1}{2}(\varphi_1+\varphi_2)+\theta_\mathrm{in}-\theta_\mathrm{out}$, of the relative phase $\theta_\mathrm{in}-\theta_\mathrm{out}$ between the two squeezers, and the average of the phase delays $\varphi_1,\varphi_2$ in the two arms of the interferometer. The detection sensitivity scales at the Heisenberg limit and, remarkably, is robust to the detector inefficiency.

Optimal Mach-Zehnder phase sensitivity with Gaussian states

We address in this work the phase sensitivity of a Mach-Zehnder interferometer with Gaussian input states. A squeezed-coherent plus squeezed vacuum input state allows us to unambiguously determine the optimal phase-matching conditions in order to maximize the quantum Fisher information. Realistic detection schemes are described and their performance compared in respect with the quantum Cram\'er-Rao bound. The core of this paper discusses in detail the most general Gaussian input state, without any apriori parameter restrictions. Prioritizing the maximization of various terms in the quantum Fisher information has the consequence of imposing the input phase-matching conditions. We discuss in detail when each scenario yields an optimal performance. Realistic detection scenarios are also considered and their performance compared to the theoretical optimum. The impact of the beam splitter types employed on the optimum phase-matching conditions is also discussed. We find a number of potentially interesting advantages of these states over the coherent plus squeezed vacuum input case.

Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors

Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI)---a proven lower bound on the distillable entanglement of a quantum state under one-way local operations and classical communication (LOCC), as our figure of merit. We evaluate a Gaussian lower bound on the RCI of the heralded state. We show that it can exceed the unlimited two-way LOCCassisted direct transmission entanglement distillation capacity of the pure loss channel. The optimal heralded Gaussian RCI with two quantum scissors is found to be significantly more than that with a single quantum scissors, albeit at the cost of decreased success probability. Our results fortify the possibility of a quantum repeater scheme for CV quantum states using the quantum scissors.

Phase estimation of phase shifts in two arms for an SU(1,1) interferometer with coherent and squeezed vacuum states**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474095, 11654005, and 11234003) and the National Key Research and Development Program of China (Grant No. 2016YFA0302000).

We theoretically study the quantum Fisher information (QFI) of the SU(1,1) interferometer with phase shifts in two arms by coherent ⊗ squeezed vacuum state input, and give the comparison with the result of phase shift only in one arm. Different from the traditional Mach–Zehnder interferometer, the QFI of single-arm case for an SU(1,1) interferometer can be slightly higher or lower than that of two-arm case, which depends on the intensities of the two arms of the interferometer. For coherent ⊗ squeezed vacuum state input with a fixed mean photon number, the optimal sensitivity is achieved with a squeezed vacuum input in one mode and the vacuum input in the other.

Fisher information of a squeezed-state interferometer with a finite photon-number resolution

Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the output ports. Here we show that for each individual $N$-photon component of the phase-matched coherent $\otimes$ squeezed vacuum input state, the classical Fisher information always saturates the quantum Fisher information. Moreover, the total Fisher information is the sum of the contributions from each individual $N$-photon components, where the largest $N$ is limited by the finite number resolution of available photon counters. Based on this observation, we provide an approximate analytical formula that quantifies the amount of lost information due to the finite photon number resolution, e.g., given the mean photon number $\bar{n}$ in the input state, over $96$ percent of the Heisenberg limit can be achieved with the number resolution larger than $5\bar{n}$.

Quantum optical metrology in the lossy SU(2) and SU(1,1) interferometers

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 coherent-squeezed state by increasing the amplifier gain of the OPA.

A scheme for Sagnac effect improvement with squeezed vacuum input and homodyne detection

There has been much interest in improving gyroscope precision with quantum technology for realizing autonomous navigation. The laser light in coherent state cannot reach higher precision under shot-noise limit (SNL) caused by vacuum zero energy fluctuation, which restricts the further improvement of optical gyroscope precision. Quantum mechanics reckons that one unused port of the beam splitter (BS) is inputted with vacuum, which results in vacuum fluctuation, while another port is inputted with the laser light in optical gyroscope. In order to compress the vacuum fluctuation, we design an experimental scheme, in which squeezed vacuum light is used as another incident light into the unused port of Sagac interferometer in optical gyroscope. We analyze the physical process of this scheme theoretically and develop the quantum balanced homodyne detection technique to retrieve the relative phase information of Sagac interferometer output. There are two most important conditions that we should pay attention to. 1) We should ensure that the phase of local oscillator light arg(α L), the phase of coherent light arg (αc) and the angle of squeezed direction arg(μν) in the squeezed vacuum light satisfy the condition, i.e., arg (α L2)-arg (μν) = πup and arg (α L)-arg (αc) = 0 when we perform quantum balanced homodyne detection technique for the best sensitivity δφ = e-GδφSNL, where G denotes the squeezed degree; 2) only by deriving the fields from one common source can we ensure coherence among the squeezed vacuum, probe and local oscillator. Although the requirements for experimental settings are strict, we can meet the requirement with careful calibration. Numerical analysis shows that this proposed scheme provides much higher precision below SNL: both sensitivity detection limit and dynamic range grow with an exponential rate as the squeezed degree grows. The current technology for squeezed vacuum generation by using two consecutive crystals with the optic axes tilted allows us to reach a value as high as G ≈ 16 of squeezed degree. Only by inputting such squeezed vacuum light into the unused port of BS in the optical gyroscope, can we attain sensitivity detection limit and dynamic range with increment by 108. Our approach is a new scheme for improving optical gyroscope with current available technology.

Coherent effect of triple-resonant optical parametric amplification inside a cavity with injection of a squeezed vacuum field

In theory, we study the quantum fluctuations of the subharmonic reflected field from a triple-resonant degenerate optical parametric amplifier (OPA) inside an optical cavity. We discuss two cases, where the linewidth of the harmonic field is either much narrower or broader than the subharmonic field. Since an electromagnetically-induced-transparency (EIT)-like effect can be simulated in a triple-resonant OPA, the output spectra from a triple-resonant OPA with a squeezed vacuum input may simulate the phenomenon of the response of an EIT medium for squeezed states. This scheme can be implemented with present experimental setups.

Optical bistability in V medium by squeezed vacuum input

We discuss the optical bistable behavior of a system of N V-type three-level atoms pumped by a coherent input field and coupled to a squeezed vacuum field by treating the optical bistability of such a system as an input-output problem. It is shown that bistability can be realized due to the squeezed vacuum input.

Effect of Squeezed Vacuum Input on Optical Bistability

The effect of squeezed vacuum input on the optical bistable behavior of a system of N three-level atoms which are simultaneously coupled to a coherent pump field and a squeezed vacuum input is investigated. It is shown that the squeezed vacuum will significantly increase the range of the optical bistability, and the bistability can be controlled by the squeezing photon number and the strength of two-photon correlation.

Optical bistability via squeezed vacuum input

We discuss the optical bistable behavior of a system of N Λ-type three-level atoms pumped by a coherent input field and coupled to a squeezed vacuum field by treating the optical bistability of such a system as an input-out problem. It is shown that bistability can be realized due to the squeezed vacuum input.

Laser generation with coloured input: II. Photon-number fluctuations of laser radiation in the presence of squeezed vacuum input

We apply the laser quantum Langevin equations derived in part I of this paper to the description of the laser intensity fluctuations when the external field entering the input - output port is in a squeezed vacuum state with finite bandwidth. We focus on the two opposite limits in which the detection time is much longer, or much shorter, than the inverse of the cavity linewidth. When there is detuning between the squeezed input and the laser frequency, the variance of the intensity fluctuations displays regular oscillations with frequency equal to the detuning. In the limit of small detection times there is the possibility of substantial reduction of the photon-number fluctuations using a squeezed input.

Atomic-dipole squeezing for arbitrarily prepared atom and field in multi-photon interaction

The atomic-dipole squeezing condition for arbitrarily prepared atomic and field states in multi-photon Jaynes-Cummings model was derived. Three special cases were discussed. For the field initially in a vacuum state and a certain eigenstate of the Susskind-Glogower phase operator, the analytical dipole squeezing conditions were obtained and the maximum squeezing values were calculated. For a squeezed vacuum input field, the dipole squeezing behaviours under the influence of the field squeezing parameterr and the phased atom were numerically treated.

Effect of a squeezed vacuum input on optical bistability.

We discuss the optical bistable behavior of a system of N two-level atoms pumped by a coherent input field and coupled to a squeezed vacuum field by treating the optical bistability of such a system as an input-output problem. We consider the equation of motion for atomic dipole moments, coupled to the cavity field and the squeezed vacuum, and the boundary condition connecting the input and output fields with the atomic lowering operator. A simple analytical expression for the influence of the squeezed vacuum input on the bistable behavior of the output field is derived by this method. The results indicate a strong influence of the squeezed vacuum input on optical bistability. The squeezed (stretched) vacuum input field tends to increase (decrease) the range of optical bistability.

Analysis of a multiphoton Jaynes-Cummings model with squeezed inputs.

An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.