Bogoliubov Modes Research Articles

Generation of microwave-optics entanglement via reservoir engineering in cavity magnonic systems

The strong microwave-optics entanglement is generated based on a cavity magnonic hybrid quantum system, where the magnon mode couples to the microwave cavity mode via magnetic dipole interaction and interacts with the optical modes via magneto-optical effects. It is shown that the microwave-optics entanglement can be achieved by the intermediate magnon mode acting as an engineered reservoir to cool the Bogoliubov mode, which consists of an optical mode and a microwave cavity mode. By optimizing the ratio of effective couplings and the dissipation of the magnon mode, the strong microwave-optics entanglement is obtained, which is far larger than that based on the coherent parametric coupling. The microwave-optics entanglement created in our model is that between microwave mode and polarized optical mode. Such entanglement which involves the degrees of freedom of polarization may have potential applications in polarization-dependent quantum information tasks.

Ground-state properties and Bogoliubov modes of a harmonically trapped one-dimensional quantum droplet

Ground-state properties and Bogoliubov modes of a harmonically trapped one-dimensional quantum droplet

Dephasing-assisted preparation of asymmetric steering in coupled quantum wells.

It is shown that the dephasing rates are usually harmful for quantum correlations in various systems. Nevertheless, we explore that the dephasing rates in the coupled quantum wells (QWs), as a major contribution of the decay processes, can assist to generate one-way Einstein-Podolsky-Rosen (EPR) steering. By applying two strong fields to drive two dipole-allowed transitions while the other transitions are coupled with two quantized modes, the asymmetric EPR steering is possible to obtain at steady state through a single-pathway dissipation in the three-well system. According to dressed-state and Bogoliubov mode transformation, we find that the dephasing rates play a role in modifying the dressed-state populations and the dissipation rate through multiple quantum interference mechanisms. The positive effect of the dephasing rates from a nanostructure on quantum correlation is expected to find potential applications in quantum information processing.

Microwave-mediated magnon–atom interactions: Two-mode higher-order squeezing of two YIG spheres

We propose an efficient scheme to realize almost perfect higher-order squeezing of two YIG spheres via microwave-mediated magnon–atom interactions. It is assumed that two microwave cavity modes are coupled to two YIG spheres by the magnetic dipole interaction and a superconducting artificial atom by the electric dipole interaction, respectively. When the microwave cavity fields are tuned to be far detuned from the dressed atomic Rabi sidebands and the magnon frequencies, the coherent coupling between two magnons and the artificial atom can be established via virtual photon exchange. We find that a pair of Bogoliubov modes composed of two magnon modes are cooled to the vacuum state through the atomic engineered dissipation, resulting in an ideal two-mode higher-order squeezing state of the YIG spheres. The solid-state device may find realistic applications in high-precision measurement and quantum sensing technology.

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.

How Infrared Singularities Affect Nambu–Goldstone Bosons at Finite Temperatures

Ordered phases realized through broken continuous symmetries embrace long-range order-parameter fluctuations as manifest in the power-law decays of both the transverse and longitudinal correlations, which are similar to those at the second-order transition point. We calculate the transverse one-loop correction to the dispersion relation of nonrelativistic Nambu-Goldstone (NG) bosons at finite temperatures, assuming that they have well-defined dispersion relations with some integer exponents. It is found that the transverse correlations make the lifetime of the NG bosons vanish right on the assumed dispersion curve below three dimensions at finite temperatures. Combined with the vanishing of the longitudinal "mass", the result indicates that the correlations generally bring both an intrinsic lifetime to the excitations and a qualitative change in the dispersion relation at long wavelengths below three dimensions at finite temperatures, unless it is protected by some conservation law. A more detailed calculation performed specifically on a single-component Bose-Einstein condensate reveals that the gapless Bogoliubov mode predicted by the perturbative treatment is modified substantially after incorporating the correlations to have (i) an intrinsic lifetime and (ii) a peak shift at long wavelengths from the linear dispersion relation. Thus, the NG bosons may be fluctuating intrinsically into and out of the ordered "vacuum" to maintain the order temporally.

Robust mechanical squeezing beyond 3 dB in a quadratically coupled optomechanical system

We demonstrate the dissipation-enabled generation of strong mechanical squeezing in a cavity optomechanical system by periodically modulating the amplitude of a single-tone laser driving the system. The Bogoliubov mode of the quadratically coupled mechanical oscillator cools down to its ground state due to optomechanical sideband cooling, which contributes to strong squeezing exceeding the 3 dB standard quantum limit. This sideband cooling mechanism is further optimized by numerically maximizing the ratio of the coupling sidebands. Then we look at the crucial role of the cavity mode dissipation in inducing enhanced squeezing. We also verify our results with the analytical solution (under adiabatic approximation) and the exact numerical solution. Compared with previous setups, the quadratic coupling between the mechanical oscillator and the optical mode gives rise to robust mechanical squeezing and strong optomechanical entanglement even for a large thermal occupancy of the mechanical mode.

Reservoir Engineering Strong Magnomechanical Entanglement via Dual‐Mode Cooling

AbstractA hybrid cavity magnomechanical system to transfer the bipartite entanglements and achieve the strong microwave photon–phonon entanglement based on the reservoir engineering approach is constructed. The magnon mode is coupled to the microwave cavity mode via magnetic dipole interaction and to the phonon mode via magnetostrictive force (optomechanical‐like). It is shown that the initial magnon‐phonon entanglement can be transferred to the photon‐phonon subspace in the case of these two interactions cooperating. In the reservoir‐engineering parameter regime, the initial entanglement is directionally transferred to the photon‐phonon subsystem, so a strong bipartite entanglement in which the magnon mode acts as the cold reservoir to effectively cool the Bogoliubov mode delocalized over the cavity and the mechanical deformation mode is obtained. Moreover, dual‐mode cooling is realized by engineering the dissipation of photon and phonon modes within the target mode, which allows entanglement to be further enhanced. The results indicate that the steady‐state entanglement is robust against temperature. The dual‐mode cooling reservoir engineering scheme can potentially be extended to other three‐mode quantum systems.

Quantum-geometric contribution to the Bogoliubov modes in a two-band Bose-Einstein condensate

We consider a weakly interacting Bose-Einstein condensate that is loaded into an optical lattice with a two-point basis and described by a two-band Bose-Hubbard model with generic one-body and two-body terms. By first projecting the system onto the lower Bloch band and then applying the Bogoliubov approximation to the resultant Hamiltonian, we show that the inverse effective-mass tensor of the superfluid carriers in the Bogoliubov spectrum has two physically distinct contributions. In addition to the usual inverse band-mass tensor that is originating from the intraband processes within the lower Bloch band, there is also a quantum-geometric contribution that is induced by the two-body interactions through the interband processes. We also discuss the conditions under which the latter contribution is expressed in terms of the quantum-metric tensor of the Bloch states, i.e., the natural Fubini-Study metric on the Bloch sphere.

Manipulation and enhancement of Einstein-Podolsky-Rosen steering between two mechanical modes generated by two Bogoliubov dissipation pathways

We consider a three-mode optomechanical system in which two mechanical oscillators are independently coupled to a cavity mode driven by two controllable lasers. By controlling the two-tone driving, one can prepare the entanglement and Einstein-Podolsky-Rosen (EPR) steering of two mechanical modes, in which the cavity mode acts as a single reservoir to cool two Bogoliubov modes. We find that the direction of EPR steering can be manipulated effectively by adjusting the damping rates and the thermal noises of two mechanical modes. In addition, we show that the entanglement and EPR steering between two mechanical modes can be enhanced by adding a parametric amplifier (PA) into the cavity. The effects of the strength and phase of the PA on the mechanical entanglement and EPR steering are analyzed and discussed in detail. Meanwhile, the additional PA can also expand the region of the one-way steering and strengthen the robustness of the entanglement and EPR steering against the thermal noise. The present scheme may provide effective resources for quantum information processing.

Tuneable Gaussian entanglement in levitated nanoparticle arrays

Optically levitated nanoparticles emerged as an interesting platform for probing fundamental physics. Quantum control of their motion (including potential shaping) predisposes them for emulating various physical systems and studying quantum phenomena with massive objects. Extending these capabilities to quantum many-body systems requires feasible strategies to couple and entangle nanoparticles directly or via an optical bus. We propose a variable, deterministic scheme to generate Gaussian entanglement in the motional steady state of levitated nanoparticles using coherent scattering. Coupling multiple nanoparticles to a common cavity mode allows cooling of a collective Bogoliubov mode; cooling multiple Bogoliubov modes (by trapping each nanoparticle in multiple tweezers, each scattering into a separate cavity mode) removes most thermal noise, leading to strong entanglement. Numerical simulations for three nanoparticles show great tuneability of entanglement with realistic experimental parameters. Our proposal paves the way towards complex motional quantum states for advanced quantum sensing protocols and many-body quantum simulations.

Manipulation and enhancement of asymmetric steering via down-converted nondegenerate photons

We investigate the asymmetric Gaussian steering with the nondegenerate parametric amplifier in a three-mode optomechanical system composed of two optical cavities and a mechanical oscillator. In the presence of the nondegenerate parametric amplifier, we find that the Gaussian steering between the auxiliary cavity and the mechanical resonator without direct interaction is significantly enhanced. By cooling the delocalized Bogoliubov modes over the auxiliary cavity and the mechanical oscillator, the optimal optomechanical entanglement and Gaussian steering can be realized and enhanced. Furthermore, we observe a wider range of parameters for the Gaussian steering with the case of cooling double delocalized modes. In addition, the magnitudes of the asymmetric Gaussian steering in two different directions can be adjusted by altering the decay rate of the auxiliary optical mode. Therefore, our proposal provides an effective method to manipulate and enhance the one-way Gaussian steering between the two modes.

Tunable second-order sideband effects in hybrid optomechanical cavity assisted with a Bose–Einstein condensate

We theoretically investigated a second-order optomechanical-induced transparency (OMIT) process of a hybrid optomechanical system (COMS), which a Bose–Einstein condensate (BEC) in the presence of atom–atom interaction trapped inside a cavity with a moving end mirror. The advantage of this hybrid COMS over a bare COMS is that the frequency of the second mode is controlled by the s-wave scattering interaction. Based on the traditional linearization approximation, we derive analytical solutions for the output transmission intensity of the probe field and the dimensionless amplitude of the second-order sideband (SS). The numerical results show that the transmission intensity of the probe field and the dimensionless amplitude of the SS can be controlled by the s-wave scattering frequency. Furthermore, the control field intensities, the effective detuning, the effective coupling strength of the cavity field with the Bogoliubov mode are used to control the transmission intensity of the probe field and the dimensionless amplitude of the SS.

Stable entanglement and one-way steering via engineering of a single-atom reservoir.

In this paper, we reexamine the quantum correlations in a four-state single-atom system in the weak coupling regime, aiming at the realization of stable entanglement and one-way steering via dissipation rather than coherent evolution process. Under the near-resonant conditions, we find out that a single atom can act as a reservoir and behave like a two-level system with a single dissipation channel, through which the composite Bogoliubov mode will evolve into a vacuum state, resulting in the appearance of stationary entanglement between two original modes. In addition, the one-way steering is generated when the symmetry is broken by choosing asymmetrical coupling constants. The present scheme may provide convenience for experimental implement and find applications in quantum information processing.

Dissipation-driven entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system.

The generation and manipulation of highly pure and strongly entangled steady state in a quantum system are vital tasks in the standard continuous-variable teleportation protocol. Especially, the manipulation implemented in integrated devices is even more crucial in practical quantum information applications. Here we propose an effective approach for creating steady-state entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system. The entanglement can be achieved by combining the processes of three beam-splitter interactions and two parametric-amplifier interactions. Due to the dissipation-driven and cavity cooling processes, the entanglement obtained can go far beyond the entanglement limit based on coherent parametric coupling. Moreover, our proposal allows the engineered bath to cool both Bogoliubov modes almost simultaneously. In this way, a highly pure and strongly entangled steady state of two microwave modes is obtained. Our finding may be significant for using the hybrid opto-electro-mechanical system fabricated on chips in various quantum tasks, where the strong and pure entanglement is an important resource.

Bogoliubov theory of the laser linewidth and application to polariton condensates

For a generic semi-classical laser dynamics in the complex Ginzburg-Landau form, we develop a Bogoliubov approach for the computation of the laser emission linewidth. Our method provides a unifying perspective of the treatments by Henry and Petermann: both broadening mechanisms are ascribed to the non-orthogonality of the Bogoliubov modes, which live in a space with doubled degrees of freedom. As an example of application, the method allows to study the interplay of driven-dissipation, interactions and spatial inhomogeneity typical of polariton condensates. The traditional theory of the Henry and Petermann factors is found to fail dramatically in the presence of sizable polariton-polariton interactions. In particular, also in a strong confining potential, the intrinsically multi-mode nature of the density fluctuations has to be considered in order to describe quantitatively phase diffusion {\em \`a la} Henry.

Remote asymmetric Einstein-Podolsky-Rosen steering of magnons via a single pathway of Bogoliubov dissipation

We propose a scheme to generate remote asymmetric Einstein-Podolsky-Rosen (EPR) steering of two magnon modes in a hybrid ferromagnet-superconductor system. In our scheme, the indirect coherent coupling between two distant magnons and a $\mathrm{\ensuremath{\Delta}}$-type superconducting atom is established via exchange of virtual photons in two dispersive cavities. As a consequence, the artificial atom acting as a reservoir can produce asymmetrical magnon-magnon steering via a single dissipation channel. Interestingly, we find that the steering directivity is determined by cooling either Bogoliubov mode selectively rather than increasing the extra noise as in conventional schemes. This provides a novel idea to prepare remote EPR steering in solid devices, which may find potential applications in quantum information processing.

Quantum fluctuations on top of a PT -symmetric Bose-Einstein condensate

We investigate the effects of quantum fluctuations in a parity-time($\mathcal{PT}$) symmetric two-species Bose-Einstein Condensate(BEC). It is found that the $\mathcal{PT}$-symmetry, though preserved by the macroscopic condensate, can be spontaneously broken by its Bogoliubov quasi-particles under quantum fluctuations. The associated $\mathcal{PT}$-breaking transitions in the Bogoliubov spectrum can be conveniently tuned by the interaction anisotropy in spin channels and the strength of $\mathcal{PT}$ potential. In the $\mathcal{PT}$-unbroken regime, the real Bogoliubov modes are generally gapped, in contrast to the gapless phonon mode in Hermitian case. Moreover, the presence of $\mathcal{PT}$ potential is found to enhance the mean-field collapse and thereby intrigue the droplet formation after incorporating the repulsive force from quantum fluctuations. These remarkable interplay effects of $\mathcal{PT}$-symmetry and interaction can be directly probed in cold atoms experiments, which shed light on related quantum phenomena in general $\mathcal{PT}$-symmetric systems.

Detecting Entanglement Structure in Continuous Many-Body Quantum Systems.

A prerequisite for the comprehensive understanding of many-body quantum systems is a characterization in terms of their entanglement structure. The experimental detection of entanglement in spatially extended many-body systems describable by quantum fields still presents a major challenge. We develop a general scheme for certifying entanglement and demonstrate it by revealing entanglement between distinct subsystems of a spinor Bose-Einstein condensate. Our scheme builds on the spatially resolved simultaneous detection of the quantum field in two conjugate observables which allows the experimental confirmation of quantum correlations between local as well as nonlocal partitions of the system. The detection of squeezing in Bogoliubov modes in a multimode setting illustrates its potential to boost the capabilities of quantum simulations to study entanglement in spatially extended many-body systems.

Supersolid phase of a spin-orbit-coupled Bose-Einstein condensate: A perturbation approach

The phase diagram of a Bose-Einstein condensate with Raman-induced spin-orbit coupling includes a stripe phase with supersolid features. In this work we develop a perturbation approach to study the ground state and the Bogoliubov modes of this phase, holding for small values of the Raman coupling. We obtain analytical predictions for the most relevant observables (including the periodicity of stripes, sound velocities, compressibility, and magnetic susceptibility) which are in excellent agreement with the exact (non perturbative) numerical results, obtained for significantly large values of the coupling. We further unveil the nature of the two gapless Bogoliubov modes in the long-wavelength limit. We find that the spin branch of the spectrum, corresponding in this limit to the dynamics of the relative phase between the two spin components, describes a translation of the fringes of the equilibrium density profile, thereby providing the crystal Goldstone mode typical of a supersolid configuration. Finally, using sum-rule arguments, we show that the superfluid density can be experimentally accessed by measuring the ratio of the sound velocities parallel and perpendicular to the direction of the spin-orbit coupling.