Squeezed Vacuum State Research Articles

Steering witnesses for unknown Gaussian quantum states

We define and fully characterize the witnesses based on second moments detecting steering in Gaussian states by means of Gaussian measurements. All such tests, which arise from linear combination of variances or second moments of canonical operators, are easily implemented in experiments. We propose also a set of linear constraints fully characterizing steering witnesses when the steered party has one bosonic mode, while in the general case the constraints restrict the set of tests detecting steering. Given an unknown quantum state we implement a semidefinite program providing the appropriate steering test with respect to the number of random measurements performed. Thus, it is a ‘repeat-until-success’ method allowing for steering detection with less measurements than in full tomography. We study the efficiency of steering detection for two-mode squeezed vacuum states, for two-mode general unknown states, and for three-mode continuous variable GHZ states. In addition, we discuss the robustness of this method to statistical errors.

Enhanced signal-to-noise ratio in quantum plasmonic image sensing including loss and varying photon number

The signal-to-noise ratio is an important quantity in signal and image analysis that gives information about the quality of the signal and/or image of interest. When plasmonic biosensors are used to study how molecules interact in intermolecular binding reactions, the output signal and/or image must be of the highest quality to get the best value from our biosensors. Images of interest in this work are images of the binding region at the metal surface of the plasmonic biosensor. Improving the signal-to-noise ratio of these signals and/or images is a key area of research that can help scientists learn more about how different molecules interact with each other. Because these molecular entities can include a wide range of biomolecules, we can investigate different types of binding interactions. In this paper, we look at a theoretical two-mode image sensing framework that we use to model the signal-to-noise ratio in images generated by a plasmonic image-based biosensor. A Krestchmann configuration-based surface resonance sensor is used as a plasmonic biosensor. In the model, an example of how BSA and an antibody called IgG1 bind to the surface of a plasmonic biosensor are examined. Traditionally, classical states of light are used as probe states in the Krestchman configuration; in this paper, quantum states of light are considered alternative probe states. The effect of using quantum states of light, such as the Fock state, squeezed displaced states, and squeezed vacuum states, on the signal-to-noise ratio of images is investigated. This work also looks at the effect of losses in the sensing environment and changes in photon numbers in the input signal on the average signal-to-noise ratio of the output of the plasmonic biosensor. The novelty in the described work lies in the exploration of using a variety quantum states of light as probe states in a plasmonic image-based biosensor, specifically in the context of improving the signal-to-noise ratio of images captured from the binding region at the metal surface accounting for the impact of losses. It was found that some quantum states improve the signal-to-noise ratio of the plasmonic biosensor output image.

Mitigating Quantum Decoherence in Force Sensors by Internal Squeezing.

The most efficient approach to laser interferometric force sensing to date uses monochromatic carrier light with its signal sideband spectrum in a squeezed vacuum state. Quantum decoherence, i.e., mixing with an ordinary vacuum state due to optical losses, is the main sensitivity limit. In this Letter, we present both theoretical and experimental evidence that quantum decoherence in high-precision laser interferometric force sensors enhanced with optical cavities and squeezed light injection can be mitigated by a quantum squeeze operation inside the sensor's cavity. Our experiment shows an enhanced measurement sensitivity that is independent of the optical readout loss in a wide range. Our results pave the way for quantum improvements in scenarios where high decoherence previously precluded the use of squeezed light. Our results hold significant potential for advancing the field of quantum sensors and enabling new experimental approaches in high-precision measurement technology.

Single and coupled cavity mode sensing schemes using a diagnostic field.

Precise optical mode matching is of critical importance in experiments using squeezed-vacuum states. Automatic spatial-mode matching schemes have the potential to reduce losses and improve loss stability. However, in quantum-enhanced coupled-cavity experiments, such as gravitational-wave detectors, one must also ensure that the sub-cavities are also mode matched. We propose what we believe to be a new mode sensing scheme, which works for simple and coupled cavities. The scheme requires no moving parts, nor tuning of Gouy phases. Instead a diagnostic field tuned to the HG20/LG10 mode frequency is used. The error signals are derived to be proportional to the difference in waist position, and difference in Rayleigh ranges, between the sub-cavity eigenmodes. The two error signals are separable by 90 degrees of demodulation phase. We demonstrate reasonable error signals for a simplified Einstein Telescope optical design. This work will facilitate routine use of extremely high levels of squeezing in current and future gravitational-wave detectors.

Surface Plasmon Polaritions via Squeezed Vacuum States

This paper investigates a dielectric under a squeezed vacuum state, a thermal field and a normal vacuum state. The dielectric atoms are considered in a three-level lambda type configuration, where a weak probe field induces and generates surface plasmon polaritons (SPPs) at the silver and dielectric interface. Therefore, to get deeper insights into the dispersion and absorption spectra, the propagation length and the skin depth, we investigate the system’s coherence. Hence, we demonstrate that the strong laser used to couple the intermediate level to the upper excited state drastically affects the generated SPPs wavelength at the interface. Additionally, the system properties are fully controlled by the average photon number, the thermal field, the normal vacuum and the squeezed vacuum state. Finally, in an attempt to elaborate a straightforward technique that manipulates the Lsp ( surface plasmon length ) distance we control the system by simultaneously tuning the phase and the control field in a particular detuning region. Our results might be of great interest to the engineering of miniature nano-photonic devices and circuits requiring sub-wavelength property.

Enhancement of the phase sensitivity with two-mode squeezed coherent state based on a Mach-Zehnder interferometer.

We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.

Enhanced entanglement and quantum teleportation of two-mode squeezed vacuum state via multistage non-Gaussian operations

The improvement of quantum features and processes, prominent as entanglement and quantum teleportation, of the two-mode squeezed vacuum state (TMSVS) in the small squeezed parameter domain is of great importance. Therefore, it has attracted the attention of scientists in the field of quantum information in recent years. In this paper, we introduce a new optical scheme to enhance the degree of entanglement and quantum teleportation fidelity of such a state using ordinary quantum devices including beam splitters and photon-number-resolving detectors. The scheme allows us to sequentially perform non-Gaussian operations, namely, photon addition, photon subtraction, quantum optical catalysis, and combinations of these techniques, into both modes of the TMSVS. The investigated results show that the degree of entanglement and fidelity in the novel two-mode non-Gaussian state is enhanced, especially in the small regions of the squeezed parameter compared with the original TMSVS and non-Gaussian states constructed from it in previous works. They also indicate that the enhanced zones recede to the small squeezed parameter areas with increasing the number of stages of the non-Gaussian effect.

Sub-Planck structures and sensitivity of the superposed photon-added or photon-subtracted squeezed-vacuum states

The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale $\ensuremath{\hbar}$, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work we introduce compasslike states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that when a significant quantity of photons is added (or subtracted), the Wigner functions of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon-addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon-subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.

How to verify identity in the continuous variable quantum system?

Continuous variable quantum cryptography has developed rapidly in recent decades, but how to verify identity in the continuous variable quantum system is still an urgent issue. To solve this problem, we propose a continuous variable quantum identification (CV-QI) protocol based on the correlation of the two-mode squeezed vacuum state and the continuous variable teleportation. The bidirectional identity verification between two participants of the communication can be achieved by the proposed CV-QI protocol. To guarantee the security, we make full use of the decoy state sequences during the whole process of the proposed CV-QI protocol. Besides, we provide the security analyses of the proposed CV-QI protocol, and analyses indicate that the security of the proposed CV-QI protocol is guaranteed.

Quantum repeater using two-mode squeezed states and atomic noiseless amplifiers

We perform a theoretical investigation into how a two-mode squeezed vacuum state, which has undergone photon loss, can be stored and purified using noiseless amplification with a collection of solid-state qubits. The proposed method may be used to probabilistically increase the entanglement between the two parties sharing the state. The proposed amplification step is similar in structure to a set of quantum scissors. However, in this work the amplification step is realized by a state transfer from an optical mode to a set of solid-state qubits, which act as a quantum memory. We explore two different applications, the generation of entangled many-qubit registers and the construction of quantum repeaters for long-distance quantum key distribution.

Quantum loss sensing with two-mode squeezed vacuum state under noisy and lossy environment

We investigate quantum advantages in loss sensing when the two-mode squeezed vacuum state is used as a probe. Following an experimental demonstration in PRX 4, 011049, we consider a quantum scheme in which the signal mode is passed through the target and a thermal noise is introduced to the idler mode before they are measured. We consider two detection strategies of practical relevance: coincidence-counting and intensity-difference measurement, which are widely used in quantum sensing and imaging experiments. By computing the signal-to-noise ratio, we verify that quantum advantages persist even under strong thermal background noise, in comparison with the classical scheme which uses a single-mode coherent state that directly suffers from the thermal noise. Such robustness comes from the fact that the signal mode suffers from the thermal noise in the classical scheme, while in the quantum scheme, the idler mode does. For a fairer comparison, we further investigate a different setup in which the thermal noise is introduced to the signal mode in the quantum schemes. In this new setup, we show that the quantum advantages are significantly reduced. Remarkably, however, under an optimum measurement scheme associated with the quantum Fisher information, we show that the two-mode squeezed vacuum state does exhibit a quantum advantage over the entire range of the environmental noise and loss. We expect this work to serve as a guide for experimental demonstrations of quantum advantages in loss parameter sensing, which is subject to lossy and noisy environment.

Unbalanced beam splitters enabling enhanced phase sensitivity of a Mach-Zehnder interferometer using coherent and squeezed vacuum states

An optical interferometer seeded by coherent and squeezed vacuum states seems to be the most promising platform for gravitational wave detection. Prior studies regarding this estimation protocol focus on the scenario in which the transmittances of two beam splitters are $\frac{1}{2}$. In this paper, with respect to the same inputs, we analyze the phase sensitivity of an unbalanced Mach-Zehnder interferometer (MZI) followed by balanced homodyne measurement. We give the optimal transmittance and demonstrate the advantage of our scheme over a balanced MZI scheme. Additionally, when the average photon number of the coherent state is dominant, the phase sensitivity of our scheme can nearly saturate the single-parameter quantum Cram\'er-Rao bound. Our results may contribute to the development of practical quantum sensing.

Simultaneous Preparation of Two Optical Cat States Based on a Nondegenerate Optical Parametric Amplifier

AbstractThe cat state, known as the superposition of coherent states, has broad applications in quantum computation and quantum metrology. Increasing the number of optical cat states is crucial to implement complex quantum information tasks based on them. Here, two optical cat states are prepared simultaneously based on a nondegenerate optical parametric amplifier. By subtracting one photon from each of two squeezed vacuum states, two odd cat states with orthogonal superposition direction in phase space are prepared simultaneously, which have similar fidelity of 60% and amplitude of 1.2. Compared with the traditional method to generate two odd optical cat states based on two degenerate optical parametric amplifiers, only one nondegenerate optical parametric amplifier is applied in this experiment, which saves half of the quantum resources of nonlinear cavities. The presented results make a step toward preparing the four‐component cat state, which has potential applications in fault‐tolerant quantum computation.

Deterministic Quantum Phase Estimation beyond N00N States

The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6) rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.

Quantum-enhanced optical precision measurement assisted by low-frequency squeezed vacuum states

Stable low-frequency squeezed vacuum states at a wavelength of 1550 nm were generated. By controlling the squeezing angle of the squeezed vacuum states, two types of low-frequency quadrature-phase squeezed vacuum states and quadrature-amplitude squeezed vacuum states were obtained using one setup respectively. A quantum-enhanced fiber Mach–Zehnder interferometer (FMZI) was demonstrated for low-frequency phase measurement using the generated quadrature-phase squeezed vacuum states that were injected. When phase modulation was measured with the quantum-enhanced FMZI, there were above 3 dB quantum improvements beyond the shot-noise limit (SNL) from 40 kHz to 200 kHz, and 2.3 dB quantum improvement beyond the SNL at 20 kHz was obtained. The generated quadrature-amplitude squeezed vacuum state was applied to perform low-frequency amplitude modulation measurement for sensitivity beyond the SNL based on optical fiber construction. There were about 2 dB quantum improvements beyond the SNL from 60 kHz to 200 kHz. The current scheme proves that quantum-enhanced fiber-based sensors are feasible and have potential applications in high-precision measurements based on fiber, particularly in the low-frequency range.

Remote Preparation of Optical Cat States Based on Gaussian Entanglement

AbstractRemote state preparation enables one to prepare and manipulate quantum state non‐locally. As an essential quantum resource, optical cat state is usually prepared locally by subtracting photons from a squeezed vacuum state. For remote quantum information processing, it is essential to prepare and manipulate optical cat states remotely based on Gaussian entanglement, which remains a challenge. Here, experimental preparation of optical cat states based on a remotely distributed two‐mode Gaussian entangled state in a lossy channel is presented. By performing photon subtraction and homodyne projective measurement at Alice's station, an optical cat state is prepared remotely at Bob's station. Furthermore, the prepared cat state is rotated by changing Alice's measurement basis of homodyne detection, which demonstrates the remote manipulation of it. By distributing two modes of the two‐mode Gaussian entangled state in lossy channels, it is demonstrated that the remotely prepared cat state can tolerate much more loss in Alice's channel than that in Bob's channel. It is also shown that cat states with amplitudes larger than 2 can be prepared by increasing the squeezing level and subtracting photon numbers. The results make a crucial step toward remote hybrid quantum information processing involving discrete‐ and continuous‐variable techniques.

Unconditional remote entanglement using second-harmonic generation and twin two-mode squeezed vacuum states

We propose a photonics-based, continuous-variable (CV) form of remote entanglement utilizing strictly second-order nonlinear optical interactions that does not require the implementation of a state-projective measurement (i.e. remote entanglement without conditioning). This scheme makes use of two separate down-converters, wherein the corresponding nonlinear crystals are driven by strong classical fields as prescribed by the parametric approximation, as well as a fully quantum mechanical model of nondegenerate second harmonic generation (SHG) whose evolution is described by the trilinear Hamiltonian of the form $\hat{H}_{\text{shg}} = i\hbar\kappa\big(\hat{a}\hat{b}\hat{c}^{\dagger} - \hat{a}^{\dagger}\hat{b}^{\dagger}\hat{c}\big)$. By driving the SHG process with the signal modes of the two down-converters, we show entanglement formation between the generated second-harmonic mode (SH-mode) and the non-interacting joint-idler subsystem without the need for any state-reductive measurements on the interacting modes.

Parity-based estimation in an SU(1,1) interferometer with photon-subtracted squeezed vacuum states

We theoretically investigate the parity-based phase estimation and the quantum Fisher information in an SU(1,1) interferometer with different phase configuration. For the parity detection, we analytically demonstrate that the signal of the measurement will hold the same for arbitrary phase configurations within the constraint of the sum of the estimated phases occur in both arms of the interferometer. When the mixing a coherent state and a photon-subtracted squeezed vacuum state (PSSVS) as the input state, we further investigate the advantage of improving phase sensitivity for such input state. Our results indicate that both phase sensitivity and resolution with the PSSVS are superior to those with the squeezed vacuum state (SVS) for a given squeezing parameter. While within a constraint on the mean photon number of these squeezed states, the PSSVS does not improve the phase sensitivity at the optimal working point ϕ=0. However, when the phase shift slightly deviates from zero, the PSSVS still holds the advantage in phase sensitivity even under the condition of the same mean photon number. Finally, we obtain the quantum Fisher information of the PSSVS and compare it with the optimal phase sensitivity.

Squeezing Limit of the Josephson Ring Modulator as a Nondegenerate Parametric Amplifier

Two-mode squeezed vacuum states are a crucial component of quantum technologies. In the microwave domain, they can be produced by Josephson ring modulator which acts as a three-wave mixing non-degenerate parametric amplifier. Here, we solve the master equation of three bosonic modes describing the Josephson ring modulator with a novel numerical method to compute squeezing of output fields and gain at low signal power. We show that the third-order interaction from the three-wave mixing process intrinsically limits squeezing and reduces gain. Since our results are related to other general cavity-based three-wave mixing processes, these imply that any non-degenerate parametric amplifier will have an intrinsic squeezing limit in the output fields.

Protection of Noise Squeezing in a Quantum Interferometer with Optimal Resource Allocation.

Interferometers are crucial for precision measurements, including gravitational waves, laser ranging, radar, and imaging. The phase sensitivity, the core parameter, can be quantum-enhanced to break the standard quantum limit (SQL) using quantum states. However, quantum states are highly fragile and quickly degrade with losses. We design and demonstrate a quantum interferometer utilizing a beam splitter with a variable splitting ratio to protect the quantum resource against environmental impacts. The optimal phase sensitivity can reach the quantum Cramér-Rao bound of the system. This quantum interferometer can greatly reduce the quantum source requirements in quantum measurements. In theory, with a 66.6% loss rate, the sensitivity can break the SQL using only a 6.0dB squeezed quantum resource with the current interferometer rather than a 24dB squeezed quantum resource with a conventional squeezing-vacuum-injected Mach-Zehnder interferometer. In experiments, when using a 2.0dB squeezed vacuum state, the sensitivity enhancement remains at ∼1.6 dB via optimizing the first splitting ratio when the loss rate changes from 0% to 90%, indicating that the quantum resource is excellently protected with the existence of losses in practical applications. This strategy could open a way to retain quantum advantages for quantum information processing and quantum precision measurement in lossy environments.