Single-Photon Optomechanics

We study an optomechanical system consisting of an optical cavity and movable mirror coupled through dispersive linear optomechanical coupling (LOC) and quadratic optomechanical coupling (QOC). We work in the resolved side band limit with a high quality factor mechanical oscillator in a strong coupling regime. We show that the presence of QOC in the conventional optomechanical system (with LOC alone) modifies the mechanical oscillator’s frequency and reduces the back-action effects on mechanical oscillator. As a result of this the fluctuations in mechanical oscillator can be suppressed below standard quantum limit thereby squeeze the mechanical motion of resonator. We also show that either of the quadratures can be squeezed depending on the sign of the QOC. With detailed numerical calculations and analytical approximation we show that in such systems, the 3 dB limit can be beaten.

In this paper we discuss how red-sideband cooling is modified in the\nsingle-photon strong-coupling regime of cavity optomechanics where the\nradiation pressure of a single photon displaces the mechanical oscillator by\nmore than its zero-point uncertainty. Using Fermi's Golden rule we calculate\nthe transition rates induced by the optical drive without linearizing the\noptomechanical interaction. In the resolved-sideband limit we find\nmultiple-phonon cooling resonances for strong single-photon coupling that lead\nto non-thermal steady states including the possibility of phonon anti-bunching.\nOur study generalizes the standard linear cooling theory.\n

Summary form only given. Due to the prospect of transferring the optical quantum control achieved with ions and atoms also to macroscopic mechanical oscillators, cavity optomechanics [1,2] has been an increasingly active research field commencing with the first demonstration of radiation pressure dynamical backaction cooling more than half a decade ago. By optimizing the optical and mechanical quality factors and operating at cryogenic temperatures, quantum-coherent coupling could be achieved [3]. Simultaneously, it has been shown that nanomechanical resonators based on photonic crystals can be advantageous, as they offer low phonon occupancies (n̅ = k<;sub>B<;/sub>T/ħΩ) due to the high vacuum optomechanical coupling rates and high mechanical frequencies in the GHz domain [4]. To fully exploit the potential of these systems, sensitive measurement techniques need to be developed.Here we present a novel route using a heterodyne measurement technique to achieve significantly improved sensitivity. Based on an optical design presented in [5], we fabricate a suspended 1 D photonic crystal cavity surrounded by 2 D photonic crystals with a band gap at 1550 nm in silicon-on-insulator (Fig. 1 (a)). Together with a mesa structure defined by photolithography, it is possible to couple the cavity with a straight tapered fiber. The loaded optical Q-factor is measured as > 104. In direct detection, we observe the mechanical breathing mode around 5.7 GHz using the 12 GHz detector 1544-A by Newport, thus placing the optical cavity in the resolved sideband limit. The low quality factor of the mechanical oscillator <; 103 is explained by the domination of anchor and surface losses but can be improved by appropriate engineering.In the heterodyne experiment, we branch the light of a tunable diode laser before the device under test (DUT). One branch is coupled in and out of the cavity using a straight tapered fiber. A shifted local oscillator is created in the second branch, offset by a tunable frequency close to the mechanical oscillator mode. The shifted LO is then combined using free space optics with the signal coming from the device and carrying the mechanically induced sideband. Afterwards, the beam is split again and both branches are sent onto a balanced heterodyne detector. Fig. 1 (c) shows the resulting measurement. The local oscillator is detuned to proof that indeed the mixed signal of the nano-mechanical mode is measured and not any other components. The down-mixed signal exhibits a SNR of nearly 20 dB, greatly exceeding the SNR in direct detection. The shown data was carried out with an unfiltered signal. Further improvement is expected from suppressing the carrier by using a fiber loop cavity or Fabry-Perot filter. The elemental demonstration of this measurement scheme paves the way towards quantum limited mechanical measurements in the GHz domain.

Cavity quantum optomechanics has emerged as a new platform for quantum science and technology with applications ranging from quantum-information processing to tests of the foundations of physics. Of crucial importance for optomechanics is the generation and verification of non-Gaussian states of motion and a key outstanding challenge is the observation of a canonical two-mode Schrödinger-cat state in the displacement of two mechanical oscillators. In this work, we introduce a pulsed approach that utilizes the nonlinearity of the radiation–pressure interaction combined with photon-counting measurements to generate this entangled non-Gaussian mechanical state, and, importantly, describe a protocol using subsequent pulsed interactions to verify the non-Gaussian entanglement generated. Our pulsed verification protocol allows quadrature moments of the two mechanical oscillators to be measured up to any finite order providing a toolset for experimental characterisation of bipartite mechanical quantum states and allowing a broad range of inseparability criteria to be evaluated. Key experimental factors, such as optical loss and open-system dynamics, are carefully analyzed and we show that the scheme is feasible with only minor improvements to current experiments that operate outside the resolved-sideband regime. Our scheme provides a new avenue for quantum experiments with entangled mechanical oscillators and offers significant potential for further research and development that utilizes such non-Gaussian states for quantum-information and sensing applications, and for studying the quantum-to-classical transition.

Coherent quantum oscillators are basic physical systems both in quantum statistical physics and quantum thermodynamics. Their realizations in lab often involve solid-state devices sensitive to changes in ambient temperature. We represent states of the solid-state optomechanical oscillator with temperature-dependent frequency by equivalent states of the mechanical oscillator with temperature-dependent energy levels. We interpret the temperature dependence as a consequence of strong coupling between the oscillator and the heat bath. We explore parameter regimes corresponding to anomalous behavior of mechanical and thermodynamic characteristics as a consequence of the strong coupling: (i) The localization and the purification induced by heating, and (ii) the negativity of two generalized heat capacities. The capacities can be used to witness non-linearity in the temperature dependency of the energy levels. Our phenomenological experimentally-oriented approach can stimulate development of new optomechanical and thermomechanical experiments exploring basic concepts of strong coupling thermodynamics.

Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.

Combing cryogenic and so-called sideband cooling promises to cool micrometre-scaled resonators to the point at which quantum effects take hold. Hope that this aim will soon be reached is boosted by the demonstration of a deformed silica microsphere that is cooled so that it contains only 37 phonons. Cooling a mechanical oscillator to its quantum ground state enables the exploration of the quantum nature and the quantum–classical boundary of an otherwise classical system1,2,3,4,5,6,7. In analogy to laser cooling of trapped ions8, ground-state cooling of an optomechanical system can in principle be achieved by radiation-pressure cooling in the resolved-sideband limit where the cavity photon lifetime far exceeds the mechanical oscillation period9,10,11. Here, we report the experimental demonstration of an optomechanical system that combines both resolved-sideband and cryogenic cooling. Mechanical oscillations of a deformed silica microsphere are coupled to optical whispering-gallery modes that can be excited through free-space evanescent coupling12,13. By precooling the system to 1.4 K, a final average phonon occupation as low as 37 quanta, limited by ultrasonic attenuation in silica, is achieved. With diminishing ultrasonic attenuation, we anticipate that the ground-state cooling can be achieved when the resonator is precooled to a few hundred millikelvin in a 3He cryostat.

We investigate an optomechanical system in which a cavity with a moving\nmirror is driven by two external fields. When the field frequencies match\nresonance conditions, we show that there exists a class of dark states of the\nmoving mirror in the single-photon strong-coupling regime. These dark states,\nwhich cause the cavity to be decoupled from the external fields, is a\nmanifestation of quantum coherence associated with the mirror's mechanical\ndegrees of freedom. We discuss the properties of the dark states and indicate\nhow they can be generated by optical pumping due to the decay of cavity field.\n

The coupling of mechanical oscillators with light has seen a recent surge of interest, as recent reviews report.[1, 2] This coupling is enhanced when confining light in an optical cavity where the mechanical oscillator is integrated as back- mirror or movable wall. At the nano-scale, the optomechanical coupling increases further thanks to a smaller optomechanical interaction volume and reduced mass of the mechanical oscillator. In view of realizing such cavity nano- optomechanics experiments, a scheme was proposed where a sub-wavelength sized nanomechanical oscillator is coupled to a high finesse optical microcavity.[3] Here we present such an experiment involving a single nanomechanical rod precisely positioned into the confined mode of a miniature Fabry-P\'erot cavity.[4] We describe the employed stabilized cavity set-up and related finesse measurements. We proceed characterizing the nanorod vibration properties using ultrasonic piezo-actuation methods. Using the optical cavity as a transducer of nanomechanical motion, we monitor optically the piezo-driven nanorod vibration. On top of extending cavity quantum electrodynamics concepts to nanomechanical systems, cavity nano-optomechanics should advance into precision displacement measurements near the standard quantum limit [5], investigation of mechanical systems in their quantum regime, non-linear dynamics [6] and sensing applications.

Mechanical oscillators which respond to radiation pressure are a promising means of transferring quantum information between light and matter. Optical–mechanical state swaps are a key operation in this setting. Existing proposals for optomechanical state swap interfaces are only effective in the resolved sideband limit. Here, we show that it is possible to fully and deterministically exchange mechanical and optical states outside of this limit, in the common case that the cavity linewidth is larger than the mechanical resonance frequency. This high-bandwidth interface opens up a significantly larger region of optomechanical parameter space, allowing generation of non-classical motional states of high-quality, low-frequency mechanical oscillators.

We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of cavity and mechanical dissipations are studied via master-equation simulations. Based on the theoretical framework, we further propose a heralded probabilistic scheme to generate mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The efficiency and fidelity of the scheme are discussed finally.

Transmon qubits are ubiquitous in the pursuit of quantum computing using superconducting circuits. However, they have some drawbacks that still need to be addressed. Most importantly, the scalability of transmons is limited by the large device footprint needed to reduce the participation of the lossy capacitive parts of the circuit. In this work, we investigate and evaluate losses in an alternative device geometry, namely, the merged-element transmon (mergemon). To this end, we replace the large external shunt capacitor of a traditional transmon with the intrinsic capacitance of a Josephson junction (JJ) and achieve an approximately 100 times reduction in qubit dimensions. We report the implementation of the mergemon using a sputtered Nb--amorphous-Si--Nb trilayer film. In an experiment below 10 mK, the frequency of the readout resonator, capacitively coupled to the mergemon, exhibits a qubit-state dependent shift in the low power regime. The device also demonstrates the single- and multi-photon transitions that represent a weakly anharmonic system in the two-tone spectroscopy. The transition spectra are explained well with master-equation simulations. A participation ratio analysis identifies the dielectric loss of the a-Si tunnel barrier and its interfaces as the dominant source for qubit relaxation. We expect the mergemon to achieve high coherence in relatively small device dimensions when implemented using a low-loss, epitaxially-grown, and lattice-matched trilayer.

For cavity-assisted optomechanical cooling experiments, in order to achieve the quantum ground state of the mechanical oscillator, the cavity bandwidth needs to be smaller than the mechanical frequency. In the literature, this is the so-called resolved-sideband or good-cavity limit, and this is based on an understanding of optomechanical dynamics. We provide a different but physically equivalent explanation of such a limit: that is, information loss due to finite cavity bandwidth. With an optimal feedback control to recover the information in the cavity output, we can surpass the resolved-sideband limit and achieve the quantum ground state. In addition, recovering this information can also significantly enhance the entanglement between the cavity mode and the mechanical oscillator. Especially when the environmental temperature is high, such optomechanical entanglement will either exist or vanish critically depending on whether information is recovered or not. This provides a vivid example of a quantum eraser in the optomechanical system.

We present an analytic solution describing the quantum state of a single photon after interacting with a moving mirror in a cavity. This includes situations when the photon is initially stored in a cavity mode as well as when the photon is injected into the cavity. In addition, we obtain the spectrum of the output photon in the resolved-sideband limit, which reveals spectral features of the single-photon strong-coupling regime in this system. We also clarify the conditions under which the phonon sidebands are visible and the photon-state frequency shift can be resolved.

In this paper, we propose a simple method to simultaneously generate the entanglement between macroscopic objects (mechanical oscillators) and entanglement between microscopic objects (photons) based on a coupled cavity-optomechanical system. We show that when the cavity-optomechanical system works in the single-photon strong-coupling regime and in the deep quantum regime, the radiation pressure of a photon which is created by the atom-cavity interaction, can directly induce these joint entangled states. Thus, no measurement on this system is required. Numerical simulation shows that the fidelity of the prepared joint entangled states can reach 0.954.