Single-photon Strong Coupling Research Articles

Prospects of cooling a mechanical resonator with a transmon qubit in c-QED setup

Hybrid devices based on the superconducting qubits have emerged as a promising platform for controlling the quantum states of macroscopic resonators. The nonlinearity added by a qubit can be a valuable resource for such control. Here we study a hybrid system consisting of a mechanical resonator longitudinally coupled to a transmon qubit. The qubit readout can be done by coupling to a readout mode like in c-QED setup. The coupling between the mechanical resonator and transmon qubit can be implemented by the modulation of the superconducting quantum interference device inductance. In such a tripartite system, we analyze the steady-state occupation of the mechanical mode when all three modes are dispersively coupled. We use the quantum noise and the Lindblad formalism to show that the sideband cooling of the mechanical mode to its ground state is achievable. We further experimentally demonstrate that measurements of the thermomechanical motion are possible in the dispersive limit, while maintaining a large coupling between qubit and mechanical mode. Our theoretical calculations suggest that single-photon strong coupling is within the experimental reach in such hybrid devices.

Optomechanical strong coupling between a single photon and a single atom

Single atoms coupled to a cavity offer unique opportunities as quantum optomechanical devices because of their small mass and strong interaction with light. A particular regime of interest in optomechanics is that of ‘single-photon strong coupling’, where motional displacements on the order of the zero-point uncertainty are sufficient to shift the cavity resonance frequency by more than its linewidth. In many cavity QED platforms, however, this is unfeasible due to the large cavity linewidth. Here, we propose an alternative route in such systems, which instead relies on the coupling of atomic motion to the much narrower cavity-dressed atomic resonance frequency. We discuss and optimize the conditions in which the scattering properties of single photons from the atom-cavity system become highly entangled with the atomic motional wave function. We also analyze the prominent observable features of this optomechanical strong coupling, which include a per-photon motional heating that is significantly larger than the single-photon recoil energy, as well as mechanically-induced oscillations in time of the second-order correlation function of the emitted light. This physics should be realizable in current experimental setups, such as trapped atoms coupled to photonic crystal cavities, and more broadly opens the door to realizing qualitatively different phenomena beyond what has been observed in optomechanical systems thus far.

Fast and Ultrasensitive Electrometer Operating at the Single-Photon Level

We demonstrate fast and ultrasensitive charge detection with a cavity-embedded Cooper pair transistor (cCPT) via dispersive readout of its Josephson inductance. We report a minimum charge sensitivity of $14$ $\mu e/\sqrt{\mathrm{Hz}}$ with a detection bandwidth on the order of $1$ MHz using $16$ attowatts of power, corresponding to the single-photon level of the cavity. In addition, our measured sensitivities are within a factor of $5$ of the quantum limit for this device. The single-photon-level sensitivity of the cCPT is comparable to that of the rf-SET, which typically operates using picowatts of power corresponding to hundreds of thousands of photons in its tank circuit. Our results support the feasibility of using the cCPT to mediate an optomechanical interaction that reaches the single-photon strong coupling regime.

Engineering Long-Lived Vibrational States for an Organic Molecule.

The optomechanical character of molecules was discovered by Raman about one century ago. Today, molecules are promising contenders for high-performance quantum optomechanical platforms because their small size and large energy-level separations make them intrinsically robust against thermal agitations. Moreover, the precision and throughput of chemical synthesis can ensure a viable route to quantum technological applications. The challenge, however, is that the coupling of molecular vibrations to environmental phonons limits their coherence to picosecond time scales. Here, we improve the optomechanical quality of a molecule by several orders of magnitude through phononic engineering of its surrounding. By dressing a molecule with long-lived high-frequency phonon modes of its nanoscopic environment, we achieve storage and retrieval of photons at millisecond timescales and allow for the emergence of single-photon strong coupling in optomechanics. Our strategy can be extended to the realization of molecular optomechanical networks.

Rare-Earth-Mediated Optomechanical System in the Reversed Dissipation Regime

Strain-mediated interaction between phonons and telecom photons is demonstrated using excited states of erbium ions embedded in a mechanical resonator. Owing to the extremely long-lived nature of rare-earth ions, the dissipation rate of the optical resonance falls below that of the mechanical one. Thus, a "reversed dissipation regime" is achieved in the optical frequency region. We experimentally demonstrate an optomechanical coupling rate g_{0}=2π×21.7 Hz, and numerically reveal that the interaction causes stimulated excitation of erbium ions. Numerical analyses further indicate the possibility of g_{0} exceeding the dissipation rates of erbium and mechanical systems, thereby leading to single-photon strong coupling. This strain-mediated interaction, moreover, involves the spin degree of freedom, and has a potential to be extended to highly coherent opto-electro-mechanical hybrid systems in the reversed dissipation regime.

Single-Photon Cooling in Microwave Magnetomechanics.

Cavity optomechanics, where photons are coupled to mechanical motion, provides the tools to control mechanical motion near the fundamental quantum limits. Reaching single-photon strong coupling would allow to prepare the mechanical resonator in non-Gaussian quantum states. Preparing massive mechanical resonators in such states is of particular interest for testing the boundaries of quantum mechanics. This goal remains however challenging due to the small optomechanical couplings usually achieved with massive devices. Here we demonstrate a novel approach where a mechanical resonator is magnetically coupled to a microwave cavity. We measure a single-photon coupling of g_{0}/2π∼3 kHz, an improvement of one order of magnitude over current microwave optomechanical systems. At this coupling we measure a large single-photon cooperativity with C_{0}≳10, an important step to reach single-photon strong coupling. Such a strong interaction allows us to cool the massive mechanical resonator to a third of its steady state phonon population with less than two photons in the microwave cavity. Beyond tests for quantum foundations, our approach is also well suited as a quantum sensor or a microwave to optical transducer.

Quantum signatures in quadratic optomechanics

We analyze quantum effects occurring in optomechanical systems where the coupling between an optical mode and a mechanical mode is quadratic in displacement (membrane-in-the-middle geometry). We show that it is possible to observe quantum effects in these systems without achieving the single-photon strong coupling regime. We find that zero-point energy causes a mechanical frequency shift, and we propose an experimental way to measure it. Further, we show that it is possible to determine the phonon statistics from the cavity transmission, and propose a way to infer the resonator's temperature based on this feature. For completeness, we revisit the case of an isolated system and show that different types of mechanical quantum states can be created, depending on the initial cavity state. In this situation, mechanical motion undergoes collapse and revivals, and we compute the collapse and revival times, as well as the degree of squeezing.

Integrated Optomechanical Arrays of Two High Reflectivity SiN Membranes.

Multielement cavity optomechanics constitutes a direction to observe novel effects with mechanical resonators. Several exciting ideas include superradiance, increased optomechanical coupling, and quantum effects between distinct mechanical modes among others. Realizing these experiments has so far been difficult, because of the need for extremely precise positioning of the elements relative to one another due to the high-reflectivity required for each element. Here we overcome this challenge and present the fabrication of monolithic arrays of two highly reflective mechanical resonators in a single chip. We characterize the optical spectra and losses of these 200 μm long Fabry-Pérot interferometers, measuring finesse values of up to 220. In addition, we observe an enhancement of the coupling rate between the cavity field and the mechanical center-of-mass mode compared to the single membrane case. Further enhancements in coupling with these devices are predicted, potentially reaching the single-photon strong coupling regime, giving these integrated structures an exciting prospect for future multimode quantum experiments.

Reaching the optomechanical strong-coupling regime with a single atom in a cavity

A major goal within the field of optomechanics is to achieve the single-photon strong coupling regime, wherein even a mechanical displacement as small as the zero-point uncertainty is enough to shift an optical cavity resonance by more than its linewidth. This goal is difficult, however, due to the small zero-point motion of conventional mechanical systems. Here, we show that an atom trapped in and coupled to a cavity constitutes an attractive platform for realizing this regime. In particular, while many experiments focus on achieving strong coupling between a photon and the atomic internal degree of freedom, this same resource also naturally enables one to obtain optomechanical strong coupling, in combination with the low mass of an atom and the isolation of its motion from a thermal environment. As an example, we show that optomechanically-induced photon blockade can be realized in realistic setups, and provide signatures of how this effect can be distinguished from the conventional Jaynes-Cummings blockade associated with the two-level nature of the atomic transition.

Cavity optomechanics in a levitated helium drop

We describe a proposal for a new type of optomechanical system based on a drop of liquid helium that is magnetically levitated in vacuum. In the proposed device, the drop would serve three roles: its optical whispering gallery modes would provide the optical cavity, its surface vibrations would constitute the mechanical element, and evaporation of He atoms from its surface would provide continuous refrigeration. We analyze the feasibility of such a system in light of previous experimental demonstrations of its essential components: magnetic levitation of mm-scale and cm-scale drops of liquid He, evaporative cooling of He droplets in vacuum, and coupling to high-quality optical whispering gallery modes in a wide range of liquids. We find that the combination of these features could result in a device that approaches the single-photon strong coupling regime, due to the high optical quality factors attainable at low temperatures. Moreover, the system offers a unique opportunity to use optical techniques to study the motion of a superfluid that is freely levitating in vacuum (in the case of $^{4}\mathrm {He}$). Alternatively, for a normal fluid drop of $^3 \mathrm{He}$, we propose to exploit the coupling between the drop's rotations and vibrations to perform quantum non-demolition measurements of angular momentum.

Strong and tunable couplings in flux-mediated optomechanics

We investigate superconducting interference device (SQUID) with two asymmetric Josephson junctions coupled to a mechanical resonator embedded in the loop of the SQUID. We quantize this system in the case when the frequency of the mechanical resonator is much lower than the cavity frequency of the SQUID and in the case when they are comparable. In the first case, the radiation pressure and cross-Kerr type interactions arise and are modified by asymmetry. Cross-Kerr type coupling is the leading term at the extremum points where radiation pressure is zero. In the second case, the main interaction is single-photon beam splitter, which exists only at finite asymmetry. Another interaction in this regime is of cross-Kerr type, which exists at all asymmetries, but generally much weaker than the beam splitter interaction. Increasing magnetic field can substantially enhance optomechanical couplings strength with the potential for the radiation pressure coupling to reach the single-photon strong coupling regime, even the ultrastrong coupling regime, in which the single-photon coupling rate exceeds the mechanical frequency.

Nonclassical correlation between optical and microwave photons in a hybrid electro-optomechanical system

A scheme to correlate optical and microwave photons is proposed in a hybrid electro-optomechanical system, where mechanical resonator is coupled to both optical and microwave fields. Analytical and numerical simulation results show that the cross-correlation function between Stokes and anti-Stokes photons strongly violates the Cauchy–Schwarz inequality, which confirms the nonclassical correlation between the optical and microwave photons. It is worth noting that the nonclassical photon pairs with vast different wavelengths, which may be useful for quantum communication, are generated under the experimentally accessible weak coupling limit rather than single-photon strong coupling regime. In addition, the protocol provides a possible route to combine the respective advantages of optical photons, microwave photons, and phonons in a hybrid electro-optomechanical system.

Two mode mechanical non-Gaussian squeezed number state in a two-membrane optomechanical system

We consider an optomechanical system with two membranes when a bichromatic laser field with red-sideband and blue-sideband frequencies is applied in the single photon strong coupling regime. It is shown that using the mode selecting method and under the Lamb–Dicke approximation, motion of membranes can evolve to single or two mode squeezed number states. By considering the environmental effect, a Wigner function is plotted for understanding the conditions that lead to the generation of non-Gaussian states. The results show that, in this system, initial states of membranes are important to generation of non-Gaussian mechanical squeezed number states.

Enhanced electromechanical coupling of a nanomechanical resonator to coupled superconducting cavities.

We investigate the electromechanical coupling between a nanomechanical resonator and two parametrically coupled superconducting coplanar waveguide cavities that are driven by a two-mode squeezed microwave source. We show that, with the selective coupling of the resonator to the cavity Bogoliubov modes, the radiation-pressure type coupling can be greatly enhanced by several orders of magnitude, enabling the single photon strong coupling to be reached. This allows the investigation of a number of interesting phenomena such as photon blockade effects and the generation of nonclassical quantum states with electromechanical systems.

Suppression of Rabi oscillations in hybrid optomechanical systems

In a hybrid optomechanical setup consisting of a two-level atom in a cavity with a pendular end-mirror, the interplay between the light field's radiation pressure on the mirror and the dipole interaction with the atom can lead to a blockade effect, which manifests itself in a suppression of Rabi oscillations in the atomic population. This effect is present when the system is in the single photon strong coupling regime and has an analogy in the photon blockade of optomechanics.

Large cooperativity and microkelvin cooling with a three-dimensional optomechanical cavity.

In cavity optomechanics, light is used to control mechanical motion. A central goal of the field is achieving single-photon strong coupling, which would enable the creation of quantum superposition states of motion. Reaching this limit requires significant improvements in optomechanical coupling and cavity coherence. Here we introduce an optomechanical architecture consisting of a silicon nitride membrane coupled to a three-dimensional superconducting microwave cavity. Exploiting their large quality factors, we achieve an optomechanical cooperativity of 146,000 and perform sideband cooling of the kilohertz-frequency membrane motion to 34±5 μK, the lowest mechanical mode temperature reported to date. The achieved cooling is limited only by classical noise of the signal generator, and should extend deep into the ground state with superconducting filters. Our results suggest that this realization of optomechanics has the potential to reach the regimes of ultra-large cooperativity and single-photon strong coupling, opening up a new generation of experiments.

Generation of motional entangled coherent state in an optomechanical system in the single photon strong coupling regime

The single-photon strong coupling in the deep-resolved sideband of the optomechanical system induces photon blockade (PB) effect. For the PB cavity, an initial mechanical coherent state evolves into superposition of phonon cat states entangled with the cavity Fock states. Measurement of the cavity photon number states produces phonon even and odd cat states. The information leakage effect of two photon states on the fidelity of cat states is calculated, it is shown that for low average phonon number this effect is negligible and decreases by increasing the two photon cavity state. The Lindblad equation is solved numerically to obtain the environmental effects on the fidelity of cat states.

Circuit electromechanics with single photon strong coupling

In circuit electromechanics, the coupling strength is usually very small. Here, replacing the capacitor in circuit electromechanics by a superconducting flux qubit, we show that the coupling among the qubit and the two resonators can induce effective electromechanical coupling which can attain the strong coupling regime at the single photon level with feasible experimental parameters. We use dispersive couplings among two resonators and the qubit while the qubit is also driven by an external classical field. These couplings form a three-wave mixing configuration among the three elements where the qubit degree of freedom can be adiabatically eliminated, and thus results in the enhanced coupling between the two resonators. Therefore, our work constitutes the first step towards studying quantum nonlinear effect in circuit electromechanics.

Entanglement of two movable mirrors with a single photon superposition state**We extend our heartiest congratulations to Margarita and Vladimir Manʼko of a magnificent 150 years and dedicate this article to them.

We propose a simple scheme to generate deterministic entanglement between two movable end mirrors in a Fabry–Perot cavity using a single photon superposition state. We derive analytically the expressions of the generated entangled states and the degree of entanglement for each state. We show that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.

Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime

Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Physical Review Letters, 109, 253601 (2012)]. Here we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime which correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation, and is based on techniques borrowed from the laser theory due to Haake's and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte-Carlo simulations, and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e. outside the single-photon strong coupling regime, for strong cavity drive, and rather large limit cycle amplitudes. The general approach taken here provides a natural starting point for further studies of quantum effects in optomechanics.