Preparing ground states and squeezed states of nanomechanical cantilevers by fast dissipation

A hybrid device consisting of a nitrogen-vacancy-center ensemble $($NVE$)$ in diamond magnetically coupled to a superconducting flux qubit is investigated. The flux qubit is suitably driven by a bichromatic microwave field to induce sidebands, which leads to the desired qubit-NVE coupling. The distinct feature of the present scheme is that the qubit decay as a resource is utilized to steer the stationary state of the NVE into a single-mode squeezed vacuum state via a dissipative repumping process.

Based on single-mode squeezed vacuum state (SVS) and Hermite-excited elementary superposition operator $ H_{m} (xa^{\dagger}+ya)$ , we induce two new quantum states, i.e., Hermite-excited squeezed vacuum state (HSVS) and Hermite-excite-orthogonalized squeezed vacuum state (HOSVS). HSVS is obtained by applying the operator on SVS and HOSVS is obtained by applying the orthogonalizer on SVS, where HSVS is just HOSVS for odd m. We study and compare mathematical and nonclassical properties for SVS, HSVS and HOSVS, including photon number distribution, Mandel’s Q parameter, quadrature squeezing, and Wigner function. Numerical results show that i) HSVS and HOSVS have only even (odd) photon components for even (odd) m; ii) HSVS and HOSVS can exhibit sub-Poissonian statistics in low-squeezing parameter regime and squeezing effect in large-squeezing parameter regime; iii) moreover, squeezing is always incompatible with sub-Poissonianity; iv) Wigner functions for HSVS and HOSVS have negative values in phase space.

Recently, photon subtraction from the single-mode squeezed vacuum state (SVS) has been explored as a technique to enhance its squeezing strength (SS). Notably, the enhancement is observed only when an even number of photons is subtracted, and this effect is limited to a specific range of the squeezing parameter r. In this paper, we introduce a novel class of single-mode nonclassical states, termed as qubit superposed SVSs (qSSVSs), via the coherent superposition of a SVS and a single-photon-subtracted SVS. The primary objective of this work is to enhance the SS for any r > 0 through the creation of these superposed states. Our analysis reveals that the qSSVSs not only improve the SS but also exhibit enhanced nonclassical features such as the negativity of Wigner function, single-mode antibunching effect, photon-number distribution, and sub-Poissonian photon statistics. Furthermore, we demonstrate that the qSSVSs provide superior phase sensitivity in a quantum Mach–Zehnder interferometer compared to the original SVS. Importantly, the generation of qSSVSs is feasible using readily available optical devices, including a beam splitter, a photodetector, and an amplitude displacement. These states hold significant potential for practical applications in quantum information science, particularly for tasks such as information encoding and processing in quantum computing systems.

In the highly non-Gaussian regime, the quantum Ziv-Zakai bound (QZZB) provides a lower bound on the available precision, demonstrating the better performance compared with the quantum Cramér-Rao bound. However, evaluating the impact of a noisy environment on the QZZB without applying certain approximations proposed by Tsang [Phys. Rev. Lett.108, 230401 (2012)10.1103/PhysRevLett.108.230401] remains a difficult challenge. In this paper, we not only derive the asymptotically tight QZZB for phase estimation with the photon loss and the phase diffusion by invoking the variational method and the technique of integration within an ordered product of operators, but also show its estimation performance for several different Gaussian resources, such as a coherent state (CS), a single-mode squeezed vacuum state (SMSVS) and a two-mode squeezed vacuum state (TMSVS). In this asymptotically tight situation, our results indicate that compared with the SMSVS and the TMSVS, the QZZB for the CS always shows the better estimation performance under the photon-loss environment. More interestingly, for the phase-diffusion environment, the estimation performance of the QZZB for the TMSVS can be better than that for the CS throughout a wide range of phase-diffusion strength. Our findings will provide an useful guidance for investigating the noisy quantum parameter estimation.

We consider distillation of squeezing in single mode squeezed vacuum state using three different probabilistic non-Gaussian operations: photon subtraction (PS), photon addition (PA) and photon catalysis (PC). To achieve this, we consider a practical model to implement these non-Gaussian operations and derive the Wigner characteristic function of the resulting non-Gaussian states. Our result shows that while PS and PC operations can distill squeezing, PA operation cannot. Furthermore, we delve into the success probabilities associated with these non-Gaussian operations and identify optimal parameters for the distillation of squeezing. Our current analysis holds significant relevance for experimental endeavors concerned with squeezing distillation.

We propose a scheme for generating squeezed states based on a superconducting hybrid system. Our system consists of a nanomechanical resonator, a superconducting flux qubit, and a superconducting transmission line resonator. Using our proposal, one can easily generate the squeezed states of the nanomechanical resonator. In our scheme, the nonlinear interaction between the nanomechanical resonator and the superconducting transmission line resonator can be implemented by the flux qubit as ‘nonlinear media’ with a tunable Josephson energy. The realization of the nonlinearity does not need any operations on the flux qubit and just needs to adiabatically keep it at the ground state, which can greatly decrease the effect of the decoherence of the flux qubit on the squeezed efficiency.

We introduce a two-mode non-Gaussian state, generated by nonlocal coherent photon-subtraction (CPS) from two single-mode squeezed vacuum states (TSSV). Its normalized factor is turned out to be related with a Legendre polynomial. We further investigate the nonclassical properties of the CPS-TSSV through cross-correlation function, antibunching effect, photon number distribution, wave function and Wigner function. It is shown that the CPS operation can produce the vortex state and can exhibit the highly nonclassical properties.

Doublet splitting due to intercell tunneling in three-Josephson-junction flux qubit

We study the eigenstates of the square of the phase operator for a single-mode field, and show that they are given as superpositions of macroscopically distinguishable phase states, which we call Schrodinger phase cats, the phase states being eigenstates of the phase operator. Those solutions that are also eigenstates of the parity operator with even parity are shown to be very similar to the squeezed vacuum states over a range of relevant parameters. Thus, it is possible to consider some squeezed vacuum states as approximate Schrodinger phase-cat states. We discuss the connections to the phase states of the SU(1, 1) phase operators for various realizations and representations.

We theoretically study macroscopic quantum entanglement in two superconducting flux qubits. To manipulate the state of two flux qubits, a Josephson junction is introduced in the connecting loop coupling the qubits. Increasing the coupling energy of the Josephson junction makes it possible to achieve relatively strong coupling between the qubits, causing two-qubit tunneling processes to be even dominant over the single-qubit tunneling processes in the states of two qubits. It is shown that due to the two-qubit tunneling processes, both the ground state and excited states of the coupled flux qubits can be a Bell type of maximally entangled state, in experimentally accessible regimes. The parameter regimes for the Bell states are discussed in terms of magnetic flux and Josephson coupling energies.

Hermite polynomial excited squeezed vacuum state: Generation and nonclassical properties

A 50∶50 beam splitter disentangles a two-mode squeezed vacuum state into two single-mode squeezed vacuum states. With the proper choice of parameters these two single-mode states will be identical. If one is passed through a device which shifts its phase, then the phases of the shifted and reference (unshifted) modes can be determined by the Vogel-Schleich technique [Phys. Rev. A44 (1991) 7642]. In this way the phase difference, i.e. the phase shift, can be measured to an accuracy of 1/N, whereN is the total number of photons coming into the beam splitter. We also propose an improved scheme involving the disentanglement of a shifted two-mode squeezed vacuum state. This leads to two shifted squeezed vacaum states at the output of the beam splitter. If one of these is passed through the phase shifter, then by performing homodyne measurements on the shifted and unshifted modes the phase shift can again be determined to an accuracy of 1/N.

A new kind of non-Gaussian quantum state is introduced by applying nonlocal coherent superposition (τa + sb) m of photon subtraction to two single-mode squeezed vacuum states, and the properties of entanglement are investigated according to the degree of entanglement and the average fidelity of quantum teleportation. The state can be seen as a single-variable Hermitian polynomial excited squeezed vacuum state, and its normalization factor is related to the Legendre polynomial. It is shown that, for τ = s, the maximum fidelity can be achieved, even over the classical limit (1/2), only for even-order operation m and equivalent squeezing parameters in a certain region. However, the maximum entanglement can be achieved for squeezing parameters with a π phase difference. These indicate that the optimal realizations of fidelity and entanglement could be different from one another. In addition, the parameter τ/s has an obvious effect on entanglement and fidelity.

Two-photon absorption (TPA) is a nonlinear optical process with wide-ranging applications from spectroscopy to super-resolution imaging. Despite this, the precise measurement and characterisation of TPA parameters are challenging due to their inherently weak nature. We study the potential of single-mode quantum light to enhance TPA parameter estimation through the quantum Fisher information (QFI). Discrete variable quantum states (defined to be a finite superposition of Fock states) are optimised to maximise the QFI for given absorption, revealing a quantum advantage compared to both the coherent state (classical) benchmark and the single-mode squeezed vacuum state. For fixed average energy n¯∈2N , the Fock state is shown to be optimal for large TPA parameters, while a superposition of vacuum and a particular Fock state is optimal for small absorption for all n¯ . This differs from single-photon absorption where the Fock state is always optimal. Notably, photon counting is demonstrated to offer optimal or nearly optimal performance compared to the QFI bound for all levels of TPA parameters for the optimised quantum probes, and their quantum advantage is shown to be robust to single-photon loss. Our findings provide insight into known limiting behaviours of Gaussian probes and their different FI scalings under photon counting ( ∝n¯2 for squeezed vacuum states versus n¯3 for coherent states). The squeezed state outperforms coherent states for small TPA parameters but underperforms in the intermediate regime, becoming comparable in the large absorption limit. This can be explained through fundamental differences between behaviours of even and odd number Fock states: the former’s QFI diverges in both large and small absorption limits, while the latter diverges only in the small absorption limit, dominating at intermediate scales.

Quantum computing and simulation based on superconducting qubits have achieved significant progress and entered the noisy intermediate-scale quantum (NISQ) era recently. Using a third qubit or object as a tunable coupler between qubits is an important step in this process. In this article, we propose a hybrid system made of superconducting qubit and a yttrium iron garnet (YIG) system as an alternative way to realize this. YIG thin films have spin wave (magnon) modes with low dissipation and reliable control for quantum information processing. Here, we propose a scheme to achieve strong coherent coupling between superconducting (SC) flux qubits and magnon modes in YIG thin film. Unlike the direct $\sqrt{N}$ enhancement factor in coupling to the Kittel mode and other spin ensembles, with $N$ the total number of spins, an additional spatial-dependent phase factor needs to be considered when the qubits are magnetically coupled with the magnon modes of finite wavelength. To avoid undesirable cancellation of coupling caused by the symmetrical boundary condition, a CoFeB thin layer is added to one side of the YIG thin film to break the symmetry. Our numerical simulation demonstrates avoided crossing and coherent transfer of quantum information between the flux qubit and the standing spin waves in YIG thin films. We show that the YIG thin film can be used as a tunable coupler between two flux qubits, which have a modified shape with small direct inductive coupling between them. Our results manifest that by cancellation of direct inductive coupling and indirect spin-wave couple of flux qubits we can turn on and off the net coupling between qubits. This bring magnonic YIG thin film into the field of quantum information processing.