Two-mode Squeezed State Research Articles

Quantum Enhanced Balanced Heterodyne Readout for Differential Interferometry.

Conventional heterodyne readout schemes are now under reconsideration due to the realization of techniques to evade its inherent 3dB signal-to-noise penalty. The application of high-frequency, quadrature-entangled, two-mode squeezed states can further improve the readout sensitivity of audio-band signals. In this Letter, we experimentally demonstrate quantum-enhanced heterodyne readout of two spatially distinct interferometers with direct optical signal combination, circumventing the 3dB heterodyne signal-to-noise penalty. Applying a high-frequency, quadrature-entangled, two-mode squeezed state, we show further signal-to-noise improvement of an injected audio band signal of 3.5dB. This technique is applicable for quantum-limited high-precision experiments, with application to searches for quantum gravity, searches for dark matter, gravitational wave detection, and wavelength-multiplexed quantum communication.

Cosmological complexity of the modified dispersion relation

Complexity will be more and more essential in high-energy physics. It is naturally extended into the very early universe. Considering the universe as a quantum chaotic system, the curvature perturbation of the scalar field is identified with the two-mode squeezed state. By solving the Schrödinger equation, one can obtain the numerical solutions of the angle parameter and squeezing parameter. The solution of the squeezing parameter mainly determines the evolution of complexity. Our numeric indicates that the complexity of the modified dispersion relation will have a non-linear pattern after the horizon exits. Meanwhile, its corresponding Lyapunov index is also larger compared with the standard case. During the inflationary period, the complexity will irregularly oscillate and its scrambling time is also shorter compared with the standard case. Since the modified dispersion relation can be dubbed as the consequences of various frameworks of quantum gravity, it could be applicable to these frameworks. Finally, one can expect the framework of quantum gravity will lead to the fruitful evolution of complexity, which guides us in distinguishing various inflationary models.

Creation of Two-Mode Squeezed States in Atomic Mechanical Oscillators.

Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the vibrational modes of trapped atoms has emerged with significant progress, featuring a high degree of control in hybridizing with spin qubits. Creating two-mode squeezed states in such a platform could enable applications that are only viable with photons. Here, we experimentally demonstrate two-mode squeezed states by employing atoms in a two-dimensional optical lattice as quantum registers. The states are generated by a controlled projection conditioned on the relative phase of two independent squeezed states. The individual squeezing is created by sudden jumps of the oscillators' frequencies, allowing generating of the two-mode squeezed states at a rate within a fraction of the oscillation frequency. We validate the states by entanglement steering criteria and Fock state analysis. Our results can be applied in other mechanical oscillators for quantum sensing and continuous-variable quantum information.

Adaptive protocols for SU(1,1) interferometers to achieve ab initio phase estimation at the Heisenberg limit

The precision of phase estimation with interferometers can be greatly enhanced using non-classical quantum states, and the SU(1,1) interferometer is an elegant scheme, which generates two-mode squeezed state internally and also amplifies the signal. It has been shown in Anderson et al (2017 Phys. Rev. A 95 063843) that the photon-number measurement can achieve the Heisenberg limit, but only for estimating a small phase shift. We relax the constraint on the range of phase by considering two adaptive protocols: one also uses the photon-number measurement with a specially tuned sequence of feedback phase; the other implements the yet-to-be-realized optimal measurement but without fine tuning.

Constructing Local Models for General Measurements on Bosonic Gaussian States.

We derive a simple sufficient criterion for the locality of correlations obtained from given measurements on a Gaussian quantum state. The criterion is based on the construction of a local-hidden-variable model that works by passing part of the inherent Gaussian noise of the state onto the measurements. We illustrate our result in the setting of displaced photodetection on a two-mode squeezed state. Here, our criterion exhibits the existence of a local-hidden-variable model for a range of parameters where the state is still entangled.

Quantum correlation of microwave two-mode squeezed state generated by nonlinearity of InP HEMT

This study significantly concentrates on cryogenic InP HEMT high-frequency circuit analysis using quantum theory to find how the transistor nonlinearity can affect the quantum correlation of the modes generated. Firstly, the total Hamiltonian of the circuit is derived, and the dynamic equation of the motion contributed is examined using the Heisenberg-Langevin equation. Using the nonlinear Hamiltonian, some components are attached to the intrinsic internal circuit of InP HEMT to address the circuit characteristics fully. The components attached are arisen due to the nonlinearity effects. As a result, the theoretical calculations show that the states generated in the circuit are mixed, and no pure state is produced. Accordingly, the modified circuit generates the two-mode squeezed thermal state, which means one can focus on calculating the Gaussian quantum discord to evaluate quantum correlation. It is also found that the nonlinearity factors (addressed as the nonlinear components in the circuit) can intensely influence the squeezed thermal state by which the quantum discord is changed. Finally, as the primary point, it is concluded that although it is possible to enhance the quantum correlation between modes by engineering the nonlinear components; however, attaining quantum discord greater than unity, entangled microwave photons, seems a challenging task since InP HEMT operates at 4.2 K.

Dissipative generation of significant amount of photon-phonon asymmetric steering in magnomechanical interfaces

A theoretical scheme is proposed to generate significant amount of photon-phonon entanglement and asymmetric steering in a cavity magnomechanical system, which is constituted by trapping a yttrium iron garnet sphere in a microwave cavity. By applying a blue-detuned microwave driving field, we obtain an effective Hamiltonian where the magnon mode acting as an engineered resevoir cools the Bogoliubov modes of microwave cavity mode and mechanical mode via a beam-splitter-like interaction. By this means, the microwave cavity mode and mechanical mode can be driven to a two-mode squeezed state in the stationary limit. Particularly, strong two-way and one-way photon-phonon asymmetric quantum steering can be obtained with even equal dissipation. It is widely divergent with the conventional proposal, where additional unbalanced losses or noises should be imposed on the two subsystems. Our finding may be significant to expand our understanding of the essential physics of asymmetric steering and extend the potential application of the cavity spintronics to device-independent quantum key distribution.

Laser-free method for creation of two-mode squeezed state and beam-splitter transformation with trapped ions

We propose a laser-free method for creation of a phonon two-mode squeezed state and a beam-splitter transformation, using time-varying electric fields and non-linear couplings between the normal modes in a linear ion crystal. Such non-linear Coulomb-mediated interactions between the collective vibrational modes arise under specific trap-frequency conditions in an ion trap. We study the quantum metrological capability for parameter estimation of the two quantum states and show that a Heisenberg limit of precision can be achieved when the initial state with n phonons evolves under the action of the beam-splitter transformation. Furthermore, we show that the phonon non-linearity and the spin-dependent force can be used for creation of a three-qubit Fredkin gate.

Phase-insensitive amplifier gain estimation at Cramér-Rao bound for two-mode squeezed state of light.

Phase-insensitive amplifiers (PIAs), as a class of important quantum devices, have found significant applications in the subtle manipulation of multiple quantum correlation and multipartite quantum entanglement. Gain is a very important parameter for quantifying the performance of a PIA. Its absolute value can be defined as the ratio of the output light beam power to the input light beam power, while its estimation precision has not been extensively investigated yet. Therefore, in this work, we theoretically study the estimation precision from the vacuum two-mode squeezed state (TMSS), the estimation precision of the coherent state, and the bright TMSS scenario, which has the following two advantages: it has more probe photons than the vacuum TMSS and higher estimation precision than the coherent state. The advantage in terms of estimation precision of the bright TMSS compared with the coherent state is researched. We first simulate the effect of noise from another PIA with gain M on the estimation precision of the bright TMSS, and we find that a scheme in which the PIA is placed in the auxiliary light beam path is more robust than two other schemes. Then, a fictitious beam splitter with transmission T is used to simulate the noise effects of propagation loss and imperfect detection, and the results show that a scheme in which the fictitious beam splitter is placed before the original PIA in the probe light beam path is the most robust. Finally, optimal intensity difference measurement is confirmed to be an accessible experimental technique to saturate estimation precision of the bright TMSS. Therefore, our present study opens a new avenue for quantum metrology based on PIAs.

Quantum entanglement for continuous variables sharing in an expanding spacetime

Detecting the structure of spacetime with quantum technologies has always been one of the frontier topics of relativistic quantum information. Here, we analytically study the generation and redistribution of Gaussian entanglement of the scalar fields in an expanding spacetime. We consider a two-mode squeezed state via a Gaussian amplification channel that corresponds to the time-evolution of the state from the asymptotic past to the asymptotic future. Therefore, the dynamical entanglement of the Gaussian state in an expanding universe encodes historical information about the underlying spacetime structure, suggesting a promising application in observational cosmology. We find that quantum entanglement is more sensitive to the expansion rate than the expansion volume. According to the analysis of quantum entanglement, choosing the particles with the smaller momentum and the optimal mass is a better way to extract information about the expanding universe. These results can guide the simulation of the expanding universe in quantum systems.

Experimental demonstration on quantum coherence evolution of two-mode squeezed state

As one of the most remarkable features of quantum mechanics, quantum coherence is regarded as an important quantum resource in the quantum information processing. The one-mode squeezed state and the two-mode squeezed state (Einstein-Podolsky-Rosen (EPR) entangled states) as the most representative examples of nonclassical states both have quantum coherence. The squeezing property of the squeezed state is described by the variance of quadrature components, and the positive partial transposition (PPT) criterion is used to describe the entanglement of the EPR entangled states. The research of the quantum coherence of Gaussian states is also a bridge between the properties of squeezing and entanglement. It has been shown that the quantum coherence with infinite-dimensional systems can be quantified by relative entropy. One of the widely used effective methods to obtain the value of quantum coherence experimentally is the quantum tomography. The covariance matrices of the quantum states are reconstructed via balanced homodyne detection and then taken into quantum coherence expression to calculate the corresponding value. The main factors affecting quantum coherence are the classical and uncorrelated noise in the actual experimental generation processing and the decoherence effect caused by the coupling between quantum resources and the surrounding environment. And the quantum coherence evolution in the generation and transmission process of the quantum resources is essential for the practical applications. Therefore, we analyze in detail the influences of the impurity of quantum resource on squeezing, entanglement and quantum coherence. The evolutions of quantum coherence of these Gaussian states in the lossy channels are demonstrated experimentally. The quantum coherence is shown to be robust against the loss in the lossy channels, which is similar to the case of squeezing and entanglement. The quantum coherences of the squeezed states and the EPR entangled states are robust against the thermal photons in the actual experimental generation processing, although the squeezing and entanglement of Gaussian states disappear at a certain number of thermal photons. Our research results provide a reference for the practical applications of quantum coherence of the squeezed state and entangled states in the lossy environment.

Speed of Evolution and Correlations in Multi-Mode Bosonic Systems.

We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert-Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

Transmission estimation at the quantum Cramér-Rao bound with macroscopic quantum light

The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cramér-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cramér-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a continuous wave bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with −8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.

Transfer of non-classical features and quantum states of light in circularly coupled waveguide arrays

We investigate the applicability of the circular arrays of coupled single-mode optical waveguides in transferring the non-classical state of light for quantum information processing. We study the nonclassical states of light, such as a single-photon Fock state, a two-photon NOON state, a single-mode squeezed state and a two-mode squeezed state as inputs to the lattice, which are key resources for various applications in the field of quantum information science. In addition, for comparison, we also examine a coherent state. We investigate the transport of non-classical features and quantum states of light from one waveguide mode to another. For the single and two-mode squeezed states, we perform a detailed study of the evolution of the squeezing. Our work highlights the potential of the circular arrays of optical waveguides platform for the transport of non-classical features and quantum states of light. We expect our results should have applications in the physical implementation of photonic quantum technologies.

Ancilla-free continuous-variable SWAP test

We propose a continuous-variable (CV) SWAP test that requires no ancilla register, thereby generalizing the ancilla-free SWAP test for qubits. In this ancilla-free CV SWAP test, the computational basis measurement is replaced by photon number-resolving measurement, and we calculate an upper bound on the error of the overlap estimate obtained from a finite Fock cutoff in the detector. As an example, we show that estimation of the overlap of pure, centered, single-mode Gaussian states of energyEand squeezed in opposite quadratures can be obtained to errorϵusing photon statistics below a Fock basis cutoffO(Eln⁡ϵ−1). This cutoff is greatly reduced toE+O(Eln⁡ϵ−1)when the states have rapidly decaying Fock tails, such as coherent states. We show how the ancilla-free CV SWAP test can be extended to many modes and applied to quantum algorithms such as variational compiling and entanglement spectroscopy in the CV setting. For the latter we also provide a new algorithm which does not have an analog in qubit systems. The ancilla-free CV SWAP test is implemented on Xanadu's 8-mode photonic processor in order to estimate the vacuum probability of a two-mode squeezed state.

Long-distance distribution of qubit-qubit entanglement using Gaussian-correlated photonic beams

We investigate the deterministic generation and distribution of entanglement in large quantum networks by driving distant qubits with the output fields of a nondegenerate parametric amplifier. In this setting, the amplifier produces a continuous Gaussian two-mode squeezed state, which acts as a quantum-correlated reservoir for the qubits and relaxes them into a highly entangled steady state. Here we are interested in the maximal amount of entanglement and the optimal entanglement generation rates that can be achieved with this scheme under realistic conditions taking, in particular, the finite amplifier bandwidth, waveguide losses, and propagation delays into account. By combining exact numerical simulations of the full network with approximate analytic results, we predict the optimal working point for the amplifier and the corresponding qubit-qubit entanglement under various conditions. Our findings show that this passive conversion of Gaussian into discrete-variable entanglement offers a robust and experimentally very attractive approach for operating large optical, microwave, or hybrid quantum networks, for which efficient parametric amplifiers are currently developed.

Wavelength conversion for single-photon polarization qubits through continuous-variable quantum teleportation

A quantum internet connects remote quantum processors that need interact and exchange quantum signals over a long distance through photonic channels. However, these quantum nodes are usually composed of quantum systems with emitted photons unsuitable for long-distance transmission. Therefore, quantum wavelength conversion to telecom is crucial for long-distance quantum networks based on optical fiber. Here we propose wavelength conversion devices for single-photon polarization qubits using continuous variable quantum teleportation, which can efficiently convert qubits between near-infrared (780/795 nm suitable for interacting with atomic quantum nodes) and telecom wavelength (1300-1500 nm suitable for long-distance transmission). The teleportation uses entangled photon sources (i.e., non-degenerate two-mode squeezed state) that can be generated by four-wave mixing in rubidium atomic vapor cells, with a diamond configuration of atomic transitions. The entangled fields can be emitted in two orthogonal polarizations with locked relative phase, making them especially suitable for interfacing with single-photon polarization qubits. Our work paves the way for the realization of long-distance quantum networks.

Two-mode squeezed state quantisation and semiclassical portraits

Quantisation with Gaussian type states offers certain advantages over other quantisation schemes, in particular, they can serve to regularise formally discontinuous classical functions leading to well defined quantum operators. In this work we define a squeezed state quantisation in two dimensions using several families of squeezed states for one- and two-mode configurations. The completeness relations of the squeezed states are exploited in order to tackle the quantisation and semiclassical analysis of a constrained position dependent mass model with harmonic potential. The effects of the squeezing parameters on the resulting operators and phase space functions are studied, and configuration space trajectories are compared between the classical and semiclassical models.

Two-mode squeezed state generation using the Bohm potential

We show that two-mode squeezed vacuum-like states may be engineered in the Bohm–Madelung formalism by adequately choosing the phase of the wave function. The difference between our wave function and the one of the squeezed vacuum states is given precisely by the phase we selected. We would like to stress that the engineering of two-mode vacuum states is possible due to the existence of the Bohm potential, and it is relevant because of its potential use in the propagation of optical fields, where it may render a variety of applications in optics. The approach to generate non-classical states, namely, two-mode squeezed states of a quantum mechanical system is one of the first applications of the Madelung–Bohm formalism.

Saturation of thermal complexity of purification

We purify the thermal density matrix of a free harmonic oscillator as a two-mode squeezed state, characterized by a squeezing parameter and squeezing angle. While the squeezing parameter is fixed by the temperature and frequency of the oscillator, the squeezing angle is otherwise undetermined, so that the complexity of purification is obtained by minimizing the complexity of the squeezed state over the squeezing angle. The resulting complexity of purification of the thermal state is minimized at non-zero values of the squeezing angle and saturates to an order one number at low frequencies, indicating that there is no additional operator cost required to build thermal mixed states when the oscillator probes length scales that are large compared to the thermal length scale. We also review applications in which thermal density matrices arise for quantum fields on curved spacetimes, including Hawking radiation and a simple model of decoherence of cosmological density perturbations in the early Universe. The complexity of purification for these mixed states also saturates as a function of the effective temperature, which may have interesting consequences for the quantum information stored in these systems.