Single-mode Squeezing Research Articles

Observation of amplitude squeezing in a constant-current-driven distributed feedback quantum dot laser with optical feedback

We illustrate the generation of single-mode amplitude squeezing in a distributed feedback quantum dot laser driven by a constant-current pump. Achieving broadband amplitude squeezing of 1.7 dB over a 10 GHz range at room temperature is realized by suppressing carrier noise and implementing optical feedback. The noise-corrected squeezing level reached 5.1 dB. Furthermore, the examination of the zero-delay second-order correlation function demonstrates the robust feedback stability of the amplitude-squeezed state in the quantum dot laser compared to a reference quantum well laser. This investigation lays the groundwork for future advancements in integrated optical quantum chips.

Describing two-mode squeezed-light experiments without two-mode entanglement or squeezing

In a recent work (Calixto and Saldanha, 2020) we have shown that experiments that produce and characterize single-mode light squeezing can be explained in a way where no single-mode squeezed light state is produced in the setup. Here we apply the same ideas to demonstrate that experiments that produce and characterize two-mode light squeezing can also be explained without the production of two-mode squeezed light states. In particular, we show that there is no entanglement between the signal and idler “twin beam” modes. This fact may be surprising, since this setup is frequently used to implement entangled-based quantum information protocols such as quantum teleportation. Our work brings an alternative view of the phenomenon. We generalize the Luis and Sánchez-Soto’s two-mode relative phase distribution (Luis and Sánchez-Soto, 1996) to treat four modes, showing that a general physical explanation for the noise reduction in the experiments is a better definition of a phase relation among the four involved optical modes: Signal, idler, and two local oscillators.

Fully guided and phase locked Ti:PPLN waveguide squeezing for applications in quantum sensing.

This work reports a fully guided setup for single-mode squeezing on integrated titanium-indiffused periodically poled nonlinear resonators. A continuous-wave laser beam is delivered and the squeezed field is collected by single-mode fibers; up to -3.17(9) dB of useful squeezing is available in fibers. To showcase the usefulness of such a fiber-coupled device, we applied the generated squeezed light in a fiber-based phase sensing experiment, showing a quantum enhancement in the signal-to-noise ratio of 0.35 dB. Moreover, our investigation of the effect of photorefraction on the cavity resonance condition suggests that it causes system instabilities at high powers.

Ultimate precision limit of noise sensing and dark matter search

The nature of dark matter is unknown and calls for a systematical search. For axion dark matter, such a search relies on finding feeble random noise arising from the weak coupling between dark matter and microwave haloscopes. We model such process as a quantum channel and derive the fundamental precision limit of noise sensing. An entanglement-assisted strategy based on two-mode squeezed vacuum is thereby demonstrated optimal, while the optimality of a single-mode squeezed vacuum is found limited to the lossless case. We propose a “nulling” measurement (squeezing and photon counting) to achieve the optimal performances. In terms of the scan rate, even with 20-decibel of strength, single-mode squeezing still underperforms the vacuum limit which is achieved by photon counting on vacuum input; while the two-mode squeezed vacuum provides large and close-to-optimum advantage over the vacuum limit, thus more exotic quantum resources are no longer required. Our results highlight the necessity of entanglement assistance and microwave photon counting in dark matter search.

Broadband squeezed microwaves and amplification with a Josephson travelling-wave parametric amplifier

Squeezing of the electromagnetic vacuum is an essential metrological technique used to reduce quantum noise in applications spanning gravitational wave detection, biological microscopy, and quantum information science. In superconducting circuits, the resonator-based Josephson-junction parametric amplifiers conventionally used to generate squeezed microwaves are constrained by a narrow bandwidth and low dynamic range. In this work, we develop a dual-pump, broadband Josephson traveling-wave parametric amplifier that combines a phase-sensitive extinction ratio of 56 dB with single-mode squeezing on par with the best resonator-based squeezers. We also demonstrate two-mode squeezing at microwave frequencies with bandwidth in the gigahertz range that is almost two orders of magnitude wider than that of contemporary resonator-based squeezers. Our amplifier is capable of simultaneously creating entangled microwave photon pairs with large frequency separation, with potential applications including high-fidelity qubit readout, quantum illumination and teleportation.

Digital quantum simulation of quantum gravitational entanglement with IBM quantum computers

We report the digital quantum simulation of a hamiltonian involved in the generation of quantum entanglement by gravitational means. In particular, we focus on a pair of quantum harmonic oscillators, whose interaction via a quantum gravitational field generates single-mode squeezing in both modes at the same time, a non-standard process in quantum optics. We perform a boson-qubit mapping and a digital gate decomposition specific for IBM quantum devices. We use error mitigation and post-selection to achieve high-fidelity, accessing a parameter regime out of direct experimental reach.

Squeezing over Two Octaves of Frequency Difference with Second Harmonic Coupling

Using the quasiprobability positive P of phase space representation, we examine the features of squeezing over two octaves of frequency difference with each octave integrating two-channel nonlinear waveguides. The second harmonic coupling of the light fields is taken into account in the current arrangement. We discovered that single-mode squeezing is decreased by second harmonic coupling.

Evolution of two-mode quantum states under a dissipative environment: Comparison of the robustness of squeezing and entanglement resources

We explore the relative robustness of single-mode squeezing and entanglement (which are quantum resources interconvertible via passive optics) for two-mode Gaussian states under different dissipative environments. When the individual modes interact with identical local baths, entanglement and squeezing decay at the same rate. However, when only one of the modes interacts with a local bath, the comparative robustness of entanglement and squeezing depends on the initial squeezing of the state. Similarly, when the system interacts with a global bath, the robustness of entanglement and squeezing depends on the initial squeezing. Thus depending on the nature of dissipative environments and the initial squeezing of the state, one can select the more robust form of resource out of squeezing and entanglement to store quantumness. This can be used to effectively enhance the performance of various quantum information processing protocols based on continuous variable Gaussian states.

Squeezing Light via Levitated Cavity Optomechanics

Squeezing light is a critical resource in both fundamental physics and precision measurement. Squeezing light has been generated through optical-parametric amplification inside an optical resonator. However, preparing the squeezing light in an optomechanical system is still a challenge for the thermal noise inevitably coupled to the system. We consider an optically levitated nano-particle in a bichromatic cavity, in which two cavity modes could be excited by the scattering photons of the dual tweezers, respectively. Based on the coherent scattering mechanism, the ultra-strong coupling between the cavity field and the torsional motion of nano-particle could be achieved for the current experimental conditions. With the back-action of the optically levitated nano-particle, the broad single-mode squeezing light can be realized in the bad cavity regime. Even at room temperature, the single-mode light can be squeezed for more than 17 dB, which is far beyond the 3 dB limit. The two-mode squeezing light can also be generated, if the optical tweezers contain two frequencies, one is on the red sideband of the cavity mode, the other is on the blue sideband. The two-mode squeezing can be maximized near the boundary of the system stable regime and is sensitive to both the cavity decay rate and the power of the optical tweezers.

Broadband complex two-mode quadratures for quantum optics

In their seminal paper, Caves and Schumaker presented a new formalism for quantum optics, intended to serve as a building block for describing two-photon processes, in terms of new, generalized qudratures. The important, revolutionary concept in their formalism was that it was fundamentally two-mode, i.e. the related observables could not be attributed to any single one of the comprising modes, but rather to a generalized complex quadrature that could only be attributed to both of them. Here, we propose a subtle, but fundamentally meaningful modification to their important work. Unlike the above proposal, we deliberately choose a frequency-agnostic definition of the two-mode quadrature, that we motivate on physical grounds. This simple modification has far-reaching implications to the formalism – the real and imaginary parts of the quadratures now coincide with the famous EPR variables, and our two-mode operators transform trivially under two-mode and single-mode squeezing operations. Their quadratic forms, which we call the “quadrature powers” are shown to succinctly generate the SU(1, 1) algebra of squeezing Hamiltonians, and correspond directly to important, broadband physical observables, that have been directly measured in experiment and are explicitly related to properties like squeezing and entanglement. This new point of view gives a fresh perspective on two-mode processes that is completely agnostic to the bandwidth, and reveals intriguing new ways for understanding and measuring broadband two-mode squeezing.

Digital quantum simulation of beam splitters and squeezing with IBM quantum computers

We present results on the digital quantum simulations of beam-splitter and squeezing interactions. The bosonic hamiltonians are mapped to qubits and then digitalized in order to implement them in the IBM quantum devices. We use error mitigation and post-selection to achieve high-fidelity digital quantum simulations of single-mode and two-mode interactions, as evidenced -- where possible -- by full tomography of the resulting states. We achieve fidelities above 90 \% in the case of single-mode squeezing with low squeezing values and ranging from 60 \% to 90 \% for large squeezing and in the more complex two-mode interactions.

On the Detection of Single-Mode Squeezed States in Kerr Nonlinear Coupler

The generation of squeezed states of light in two guided waves Kerr nonlinear coupler (KNLC) was examined using both the analytical perturbative (AP) and the short-time approximation (STA) method. A comparative analysis between these two methods is provided. We have found that, at certain combinations of input parameters, the STA method may not be able to detect the generation of squeezed states of light in the current KNLC system. Consequently, some essential physics could be lost. On the other hand, for the AP method, all time-dependent terms are included in the mode solutions which improves its sensitivity to detect the generation of squeezed states.

Nonclassicality of Photon Added Bipartite Glauber Lachs State

Mixture of coherent state with thermal noise is known as the Glauber Lachs state, which is taken into consideration. Nonlocal photon addition is imposed on the two mode Glauber Lachs state by the application of bosonic creation operators. This nonlocal photon addition induces nonclassicality, revealed in the single mode and two mode squeezing properties. The ratio of the coherent noise to thermal noise is the key factor in observing the nonclassical features. The tolerance limit of the noise for the nonclassicality is discussed in single mode squeezing and two mode squeezing quadrature operators. The results show that the squeezing properties are less pronounced even for the low level of thermal noise.

General solution of the time evolution of two interacting harmonic oscillators

We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry. In particular, we use this result to completely characterize the dynamics of the two oscillators interacting in the ultrastrong coupling regime with additional single-mode squeezing on both oscillators, as well as higher order terms. Furthermore, we compute quantities of interest, such as the average number of excitations and the correlations that are established between the two subsystems due to the evolution. We find that this model predicts a second order phase transition and we compute the critical exponents and the critical value. We also provide an exact decoupling of the time evolution in terms of simple quantum optical operations, which can be used for practical implementations and studies. Finally, we show how our techniques can be extended to include more oscillators and higher order interactions.

Optical estimation of unitary Gaussian processes without phase reference using Fock states

Since a general Gaussian process is phase-sensitive, a stable phase reference is required to take advantage of this feature. When the reference is missing, either due to the volatile nature of the measured sample or the measurement’s technical limitations, the resulting process appears as random in phase. Under this condition, we consider two single-mode Gaussian processes, displacement and squeezing. We show that these two can be efficiently estimated using photon number states and photon number resolving detectors. For separate estimation of displacement and squeezing, the practical estimation errors for hundreds of probes’ ensembles can saturate the Cramér–Rao bound even for arbitrary small values of the estimated parameters and under realistic losses. The estimation of displacement with Fock states always outperforms estimation using Gaussian states with equivalent energy and optimal measurement. For estimation of squeezing, Fock states outperform Gaussian methods, but only when their energy is large enough. Finally, we show that Fock states can also be used to estimate the displacement and the squeezing simultaneously.

Enhanced noise resilience of the surface–Gottesman-Kitaev-Preskill code via designed bias

We study the code obtained by concatenating the standard single-mode Gottesman-Kitaev-Preskill (GKP) code with the surface code. We show that the noise tolerance of this surface-GKP code with respect to (Gaussian) displacement errors improves when a single-mode squeezing unitary is applied to each mode assuming that the identification of quadratures with logical Pauli operators is suitably modified. We observe noise-tolerance thresholds of up to $\sigma\approx 0.58$ shift-error standard deviation when the surface code is decoded without using GKP syndrome information. In contrast, prior results by Fukui et al. and Vuillot et al. report a threshold between $\sigma\approx 0.54$ and $\sigma\approx 0.55$ for the standard (toric-, respectively) surface-GKP code. The modified surface-GKP code effectively renders the mode-level physical noise asymmetric, biasing the logical-level noise on the GKP-qubits. The code can thus benefit from the resilience of the surface code against biased noise. We use the approximate maximum likelihood decoding algorithm of Bravyi et al. to obtain our threshold estimates. Throughout, we consider an idealized scenario where measurements are noiseless and GKP states are ideal. Our work demonstrates that Gaussian encodings of individual modes can enhance concatenated codes.

Quantum-Enhanced Fiber-Optic Gyroscopes Using Quadrature Squeezing and Continuous-Variable Entanglement

We evaluate the fundamental performance of a fiber-optic gyroscope (FOG) design that is enhanced by the injection of a quantum-optical squeezed vacuum. In the presence of fiber loss, we compute the optimum attainable enhancement below the standard quantum limit in terms of the angular velocity estimator variance from a homodyne measurement. We find that currently realizable amounts of single-mode squeezing are sufficient to access the maximum quantitative improvement, but that this gain in maximum rotation sensitivity is limited to a marginal constant factor. We then propose an entanglement-enhanced FOG design that segments a fixed amount of available fiber into multiple fiber interferometers and feeds this sensor array with a multimode-entangled squeezed vacuum resource. Our design raises the fundamental improvement in sensitivity to an appreciable factor of $e\ensuremath{\approx}2.718$.

Stabilization and operation of a Kerr-cat qubit.

Quantum superpositions of macroscopically distinct classical states-so-called Schrödinger cat states-are a resource for quantum metrology, quantum communication and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors1,2. However, several challenges have to be overcome for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here we experimentally demonstrate a method for the generation and stabilization of Schrödinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing1,3 in a superconducting microwave resonator4. We show an increase in the transverse relaxation time of the stabilized, error-protected qubit of more than one order of magnitude compared with the single-photon Fock-state encoding. We perform all single-qubit gate operations on timescales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control and robustness against errors, which is intrinsic to stabilized macroscopic states, as well as the potential of of these states as resources in quantum information processing5-8.

Optimal estimation with quantum optomechanical systems in the nonlinear regime

We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a single-mode mechanical squeezing term. By using a recently developed method to solve the dynamics of this system, we derive a general expression for the quantum Fisher information and demonstrate its applicability through three concrete examples: estimation of the strength of a nonlinear light-matter coupling, the strength of a time-modulated mechanical displacement, and a single-mode mechanical squeezing parameter, all of which are modulated at resonance. Our results can be used to compute the sensitivity of a nonlinear optomechanical system to a number of external and internal effects, such as forces acting on the system or modulations of the light--matter coupling.

Time-evolution of nonlinear optomechanical systems: interplay of mechanical squeezing and non-Gaussianity

We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the non-Gaussian state and its closest Gaussian reference state. We find that the addition of a constant mechanical squeezing term to the standard optomechanical Hamiltonian generally decreases the overall non-Gaussian character of the state. For sinusoidally modulated squeezing, the two second-order differential equations mentioned above take the form of the Mathieu equation. We derive perturbative solutions for a small squeezing amplitude at parametric resonance and show that they correspond to the rotating-wave approximation at times larger than the scale set by the mechanical frequency. We find that the non-Gaussianity of the state increases with both time and the squeezing parameter in this specific regime.