Squeezed Vacuum State Research Articles

Supersensitivity of Kerr phase estimation with two-mode squeezed vacuum states

We analytically investigate the sensitivity of Kerr nonlinear phase estimation in a Mach-Zehnder interferometer with two-mode squeezed vacuum states. We find that such a metrological scheme could access a sensitivity scaling over the Boixo et al.'s generalized sensitivity limit [S. Boixo et al., Phys. Rev. Lett. 98, 090401 (2007)], which is saturable with celebrated NOON states. We also show that parity detection is a quasioptimal measurement which can nearly saturate the quantum Cram\'er-Rao bound in the aforementioned situation. Moreover, we further clarify the supersensitive performance observed in the above scheme is due to the restriction of Boixo et al.'s generalized sensitivity limit (BGSL) to probe states with fixed photon numbers. To conquer this problem, we generalize the BGSL into the case with probe states of a fluctuating number of photons, to which our scheme belongs.

Oscillatory amplitude of stochastic gravitational wave spectrum

Primordial gravitational waves generated from early universe are placed in the squeezed vacuum state and the resulting stochastic background is studied for various models of the expanding universe. The quantum effect on the stochastic gravitational waves leads to overall enhancement of the amplitude and spectral energy density when compared to those in the absence of squeezing effect with continued increase in the amplitude in the accelerating stage and oscillatory behavior at higher frequency range of the spectrum in the accelerating universe. Through the quantum effect, it is also found that the reheating phenomenon affects the entire spectrum. The results of the present study may be useful to test the possibility of detection of the stochastic gravitational waves by current and future gravitational wave detectors and whether these waves exist in the squeezed vacuum state.

Entanglement, nonlocal features, quantum teleportation of two-mode squeezed vacuum states with superposition of photon-pair addition and subtraction operations

In this paper, we introduce new nonclassical states called two-mode squeezed vacuum states with superposition of photon-pair addition and subtraction operations (TMSVSs-SPPASOs) by adding and subtracting pairs of photons to a two-mode squeezed vacuum state (TMSVS). It is shown that the superposition operations of photon-pair added and subtracted can enhance the degree of entanglement of the TMSVSs-SPPASOs by using the linear entropy criterion. Besides, the EPR correlation and the EPR steering in the TMSVSs-SPPASOs can be improved compared with the original TMSVS. In particular, the manifestation of these features becomes more obvious in the small region of the squeezing parameter r in the TMSVSs-SPPASOs. By using the TMSVSs-SPPASOs as entanglement resources, the quantum teleportation process of a qubit-type single-mode state is studied in detail. Based on the average fidelity Fav, it indicates that the quantum teleportation process is ideally successful as Fav approaches the unit when r is high. More importantly, the average fidelity Fav can be enhanced by increasing the number of photon pairs added or subtracted. Finally, we propose experimental schemes for generating these states by using quantum optical devices.

Wave–particle complementarity: detecting violation of local realism with photon-number resolving weak-field homodyne measurements

Nowadays photon-number resolving weak-field homodyne measurements allow realization of emblematic gedankenexperiments revealing correlations of optical fields. This covers 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. Proving Bell nonclassicality of such correlations demands measurements of complementary observables. We show that typical arrangement of weak-field homodyne detection with measurement settings defined by phases of local oscillators of constant strength does not provide enough complementarity for confirming Bell nonclassicality. In the case of experiment (a) we provide an exact local hidden variable model restoring all quantum probabilities, whereas in the case of experiment (b) we show that the claims of its nonclassicality are unfounded. A full complementarity of wave aspects vs particle (number) can be achieved in a measurement situation in which respectively the local oscillators are on or off. This is shown to lead to an operational scenario, in the case of both experiments (a) and (b), which reveals indisputable violations of local realism. Such schemes may find possible applications in device-independent quantum protocols.

Observation of Squeezed States of Light in Higher-Order Hermite-Gaussian Modes with a Quantum Noise Reduction of up to 10dB.

Mirror thermal noise will be a main limitation for the sensitivities of the next-generation ground-based gravitational-wave detectors (Einstein Telescope and Cosmic Explorer) at signal frequencies around 100Hz. Using a higher-order spatial laser mode instead of the fundamental mode is one proposed method to further mitigate mirror thermal noise. In the current detectors, quantum noise is successfully reduced by the injection of squeezed vacuum states. The operation in a higher-order mode would then require the efficient generation of squeezed vacuum states in this mode to maintain a high quantum noise reduction. In our setup, we generate continuous-wave squeezed states at a wavelength of 1064nm in the fundamental and three higher-order Hermite-Gaussian modes up to a mode order of 6 using a type-I optical parametric amplifier. We present a significant milestone with a quantum noise reduction of up to 10dB at a measurement frequency of 4MHz in the higher-order modes and pave the way for their usage in future gravitational-wave detectors as well as in other quantum noise limited experiments.

Phase locking of squeezed vacuum generated by a single-pass optical parametric amplifier.

In high-precision optical measurements, squeezed vacuum states are a promising resource for reducing the shot noise. To utilize a squeezed vacuum, it is important to lock the phase of the local oscillator (LO) to the squeezed light. The coherent control sideband (CCSB) scheme has been established for the precise phase locking, while the previous CCSB scheme was designed for the squeezed vacuum generated with an optical parametric oscillator (OPO). Thus the previous CCSB scheme is not applicable to squeezing by a single-pass optical parametric amplifier (OPA), which is attractive for generating broadband squeezed vacuum states. In this study, we propose a variant of CCSB scheme, which is applicable to the squeezing by single-pass OPA. In this scheme, we inject pump light and frequency-shifted signal light into an OPA crystal in the same way as the previous CCSB scheme. The parametric process in the OPA crystal generates a squeezed vacuum, amplifies the signal light, generates an idler light, and causes the pump depletion reflecting the interference of the amplified signal light and the idler light. Through the lock-in detection of the pump depletion, we can phase-lock the injected signal light to the pump light. Then, after the heterodyne detection of the signal and the idler light, we get the error signal of LO and realize the precise phase locking of LO to the squeezed quadrature. We show the feasibility of the proposed scheme by deriving the signal-to-noise ratio (SNR) of the modulated pump signal. We experimentally demonstrate the proposed scheme on pulsed squeezing by a single-pass OPA.

Quantum state engineering using weak measurements

State preparation via postselected weak measurement in three wave mixing process is studied. Assuming the signal input mode prepared in a vacuum state, coherent state or squeezed vacuum state, separately, while the idler input prepared in weak coherent state and passing the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of idler beam's path, the signal output channel is prepared in single-photon Fock state, single-photon-added coherent state or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties including squeezing, signal amplification, second order correlation and Wigner functions of the weak measurement based output states are also investigated. Our scheme promising to provide alternate new effective method for producing useful nonclassical states in quantum information processing.

Construction of Touchard polynomial’s Photon Added Squeezing Vacuum State and its Nonclassical Properties

Construction of Touchard polynomial’s Photon Added Squeezing Vacuum State and its Nonclassical Properties

Cavity enhanced parametric homodyne detection of a squeezed quantum comb.

A squeezed state with higher-order sidebands is a valuable quantum resource for channel multiplexing quantum communication. However, balanced homodyne detection used in nonclassical light detection has a trade-off performance between the detection bandwidth and clearance, in which the verification of a highly squeezing factor faces a challenge. Here, we construct two optical parametric amplifiers with cavity enhancement; one is for the generation of a -10.5 dB squeezed vacuum state, and the other is for all-optical phase-sensitive parametric homodyne detection. Finally, -6.5 dB squeezing at the carrier with 17 pairs of squeezing sidebands (bandwidth of 156 GHz) is directly and simultaneously observed. In particular, for the cavity-enhanced parametric oscillation and detection processes, we analyze the limiting factors of the detectable bandwidth and measurement deviation from the generated value, which indicates that the length difference and propagation loss between two optical parametric amplifiers should be as small as possible to improve the detection performance. The experimental results confirm our theoretical analysis.

Dynamical Casimir effect via modulated Kerr or higher-order nonlinearities

We show two examples in which the dynamical Casimir effect can be achieved by modulating the Kerr or higher-order nonlinearities. In the first case the cavity field is coupled to an arbitrary number of qubits or a harmonic oscillator via the dipole interaction. In the second case, the modulation of the nonlinearities is accompanied by the off-resonance modulation of the cavity frequency. We present the analytic description of the phenomenon and supplement it with numeric simulations, demonstrating that photons can be created from vacuum and the resulting hyper-Poissonian photon statistics is very different from the squeezed vacuum state.

Coherence of quantum states after noiseless attenuation

Attenuating a quantum state using a beam splitter will introduce noise and decoherence. Here we show that heralding techniques can be used to attenuate Schr\"odinger cat states and squeezed vacuum states without any noise or decoherence [Mi\v{c}uda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Noiseless attenuation also preserves quantum interference effects in nonclassical states such as squeezed vacuum states.

Enhancement of spin noise spectroscopy of rubidium atomic ensemble by using the polarization squeezed light.

We measured the spin noise spectroscopy (SNS) of rubidium atomic ensemble with two different kinds of atomic vapor cells (filled with buffer gas or coated with paraffin film on the inner wall) and demonstrated the enhancement of the signal-to-noise ratio (SNR) by using polarization squeezed state (PSS) of 795-nm light field with Stokes operator S Λ 2 squeezed. The PSS is prepared by locking the relative phase between the squeezed vacuum state of light obtained with a sub-threshold optical parametric oscillator and the orthogonally polarized local oscillator beam by means of the quantum noise lock. Under the same conditions, the PSS can be employed not only to improve the SNR, but also to keep the full width at half maximum (FWHM) of SNS, compared with the case of using the polarization coherent state (PCS), enhancement of SNR is positively correlated with the squeezing level of the PSS. With increasing probe laser power and atomic number density, the SNR and FWHM of SNS will increase correspondingly. With the help of the PSS of the Stokes operator S Λ 2, quantum improvements of both the SNR and FWHM of SNS signal has been demonstrated by controlling optical power of polarization squeezed light beam or atomic number density in our experiments.

Teleportation-based noiseless quantum amplification of coherent states of light.

We propose and theoretically analyze a teleportation-based scheme for the high-fidelity noiseless quantum amplification of coherent states of light. In our approach, the probabilistic noiseless quantum amplification operation is encoded into a suitable auxiliary two-mode entangled state and then applied to the input coherent state via continuous-variable quantum teleportation. The scheme requires conditioning on the outcomes of homodyne measurements in the teleportation protocol. In contrast to high-fidelity noiseless quantum amplifiers based on combination of conditional single-photon addition and subtraction, the present scheme requires only photon subtraction in combination with auxiliary Gaussian squeezed vacuum states. We first provide a pure-state description of the protocol which allows us to to clearly explain its principles and functioning. Next we develop a more comprehensive model based on phase-space representation of quantum states, that accounts for various experimental imperfections such as excess noise in the auxiliary squeezed states or limited efficiency of the single-photon detectors that can only distinguish the presence or absence of photons. We present and analyze predictions of this phase-space model of the noiseless teleamplifier.

The “Squeeze Laser”

The level of quantum noise in measurements is bounded from below by the Heisenberg uncertainty principle, but it can be unequally distributed between two non-commuting observables — it can be “squeezed”. Since 2019, all gravitational-wave observatories have been using squeezed light for increasing the astronomical reach. Squeezed laser light is efficiently produced by degenerate parametric down-conversion in a nonlinear crystal located inside an optical resonator. A spontaneously generated initial pair of indistinguishable photons is amplified to a squeezed vacuum state. Overlapped with bright coherent light, the photo electric measurement shows a sub-Poissonian photon statistics. Squeezed states have ample applications in nonlocal quantum sensing, device-independent quantum key distribution, and quantum computing. Here, we present our continuous-wave 1550 nm ‘squeeze laser’ with a footprint of 80 cm × 80 cm. The well-defined output beam has an interference contrast of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\gtrsim 99\%$</tex-math></inline-formula> with an overlapped 10 mW beam being in an almost perfect TEM00 mode. The interference result shows 13 dB squeezing of the photon shot noise in balanced detection.

A Squeezed Vacuum State Laser with Zero Diffusion from Cavity Losses

AbstractA method for building a squeezed vacuum state laser with zero diffusion from cavity losses is proposed. The method results from the introduction of a particular reservoir engineering technique into the laser theory, with the construction of an effective atom‐field interaction. By building an isomorphism between the cavity field operators in both the effective and the Jaynes–Cummings interactions, the equations of the effective laser are then derived directly from conventional laser theory. The distinctive characteristic of the laser method is that the required nonlinearity for light squeezing, usually achieved through a χ(2) crystal, is here replaced by the atom‐field effective interaction itself; the same nonlinearity needed for achieving a nonequilibrium steady state. The method can be extended for the construction of other nonclassical state lasers, and the present squeezed vacuum laser can contribute to the newly emerging field of gravitational wave interferometry.

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

In the present paper, we study the influence of non-commutativity on entanglement in a system of two oscillators-modes in interaction with its environment. The considered system is a two-dimensional harmonic oscillator in non-commuting spatial coordinates coupled to its environment. The dynamics of the covariance matrix, the separability criteria for two Gaussian states in non-commutative space coordinates, and the logarithmic negativity are used to evaluate the quantum entanglement in the system, which is compared to the commutative space coordinates case. The result is applied for two initially entangled states, namely the squeezed vacuum and squeezed thermal states. It can be observed that the phenomenon of entanglement sudden death appears more early in the system for the case of squeezed vacuum state than in the case of squeezed thermal state. Thereafter, it is also observed that non-commutativity effects lead to an increasing of entanglement of initially entangled quantum states, and reduce the separability in the open quantum system. It turns out that a separable state in the usual commutative quantum mechanics might be entangled in non-commutative extension.

Non-Gaussian operations in measurement-device-independent quantum key distribution

Non-Gaussian operations in continous variable (CV) quantum key distribution (QKD) have been limited to photon subtraction on squeezed vacuum states only. This is mainly due to the ease of calculating the covariance matrix representation of such states. In this paper we study the effects of general non-Gaussian operations corresponding to photon addition, catalysis and subtraction on squeezed coherent states on CV measurement device independent (MDI) QKD. We find that non-Gaussianity coupled with coherence can yield significantly longer transmission distances than without. Particularly we observe that zero photon catalysis on two mode squeezed coherent state (TMSC) is an optimial choice for CV MDI QKD, while single photon subtraction is also a good candidate; both of them offering nearly 70 km of transmission distances. We also derive a single generalized covariance matrix for the aforementioned states which will be useful in several other aspects of CV quantum information processing.

Scalable multiphoton quantum metrology with neither pre- nor post-selected measurements

The quantum statistical fluctuations of electromagnetic fields establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here, we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric downconversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling, and quantum networks.

Phase-sensitive manipulation of squeezed vacuum via a dual-recycled Michelson interferometer.

The injection of squeezed vacuum state is an indispensable technology for the next generation gravitational wave observatory, which will open up a much larger window to the universe. After analyzing the absorption and dispersion properties of the reflected field of the dual-recycled Michelson interferometer (DRMI), we propose the phase-sensitive manipulation scheme of squeezed vacuum by utilizing the coupled-resonator-induced transparency in a dual-recycled Michelson interferometer (DRMI). In this way, the rotation frequency of squeezing ellipse can be finely tuned by the coupling strength, which overcome the limitation of the current solution (with a fixed rotation frequency) that employs a Fabry-Perot optical cavity as phase-sensitive manipulation element. This work will unleash the potential applications for quantum metrology beyond the shot noise limit.

How squeezed states both maximize and minimize the same notion of quantumness

Beam splitters are routinely used for generating entanglement between modes in the optical and microwave domains, requiring input states that are not convex combinations of coherent states. This leads to the ability to generate entanglement at a beam splitter as a notion of quantumness. A similar, yet distinct, notion of quantumness is the amount of entanglement generated by two-mode squeezers (i.e., four-wave mixers). We show that squeezed-vacuum states, paradoxically, both minimize and maximize these notions of quantumness, with the crucial resolution of the paradox hinging upon the relative phases between the input states and the devices. Our notion of quantumness is intrinsically related to eigenvalue equations involving creation and annihilation operators, governed by a set of inequalities that leads to generalized cat and squeezed-vacuum states.