Kjetil Borkje

Single-photon optomechanics.

Optomechanics experiments are rapidly approaching the regime where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. We show that in this limit the power spectrum has multiple sidebands and that the cavity response has several resonances in the resolved-sideband limit. Using master-equation simulations, we also study the crossover from the weak-coupling many-photon to the single-photon strong-coupling regime. Finally, we find non-Gaussian steady states of the mechanical oscillator when multiphoton transitions are resonant. Our study provides the tools to detect and take advantage of this novel regime of optomechanics.

Signatures of Nonlinear Cavity Optomechanics in the Weak Coupling Regime

We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red detuned by twice the mechanical frequency from the cavity resonance frequency makes two-phonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong laser drive is detuned by half the mechanical frequency, optomechanically induced transparency also occurs due to resonant two-photon processes. The cavity response to a second probe drive is in this case nonlinear in the probe power. These effects should be observable with optomechanical coupling strengths that have already been realized in experiments.

Proposal for entangling remote micromechanical oscillators via optical measurements.

We propose an experiment to create and verify entanglement between remote mechanical objects by use of an optomechanical interferometer. Two optical cavities, each coupled to a separate mechanical oscillator, are coherently driven such that the oscillators are laser cooled to the quantum regime. The entanglement is induced by optical measurement and comes about by combining the output from the two cavities to erase which-path information. It can be verified through measurements of degrees of second-order coherence of the optical output field. The experiment is feasible in the regime of weak optomechanical coupling. Realistic parameters for the membrane-in-the-middle geometry suggest entangled state lifetimes on the order of milliseconds.

Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime

We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser beam are recorded simultaneously via a heterodyne measurement. The oscillator’s mean phonon number ¯ n is inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 ± 0.22 (corresponding to a mode temperature T = 28 ± 7 μ K). We also infer¯ n from the calibrated area of each of the two sidebands, and from the oscillator’s total damping. The values of ¯ n inferred from these four methods are in close agreement. The behavior of the sidebands as a function of the oscillator’s temperature agrees well with theory that includes the quantum fluctuations of both the cavity field and the mechanical oscillator.

Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency

We present a scheme for cooling mechanical motion to the ground state in an optomechanical system. Unlike standard sideband cooling, this scheme applies to the so-called unresolved sideband regime, where the resonance frequency of the mechanical mode is much smaller than the cavity linewidth. Ground state cooling becomes possible when assuming the presence of an additional, auxiliary mechanical mode and exploiting the effect of optomechanically induced transparency. We first consider a system where one optical cavity interacts with two mechanical modes, and show that ground state cooling of the unresolved mechanical mode is possible when the auxiliary mode is in the resolved sideband regime. We then present a modified setup involving two cavity modes, where both mechanical modes are allowed to be in the unresolved sideband regime.

Detecting Majorana bound states by nanomechanics

We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a one-dimensional topological superconductor, implemented, for instance, using a semiconducting wire placed on top of an s-wave superconductor. The detector makes use of an oscillating electrode, which can be realized using a doubly clamped metallic beam, tunnel coupled to one edge of the topological superconductor. We find that a measurement of the nonlinear differential conductance provides the necessary information to uniquely identify Majorana bound states.

Cooling in the single-photon strong-coupling regime of cavity optomechanics

In this Rapid Communication we discuss how red-sideband cooling is modified in the single-photon strong-coupling regime of cavity optomechanics where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. Using Fermi`s golden rule we calculate the transition rates induced by the optical drive without linearizing the optomechanical interaction. In the resolved-sideband limit we find multiple-phonon cooling resonances for strong single-photon coupling that lead to nonthermal steady states including the possibility of phonon antibunching. Our study generalizes the standard linear cooling theory.

Detection of qubit-oscillator entanglement in nanoelectromechanical systems

Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg uncertainty limit. Therefore, it is just a question of time before we will routinely see true quantum effects in nanomechanical systems. One of the hallmarks of quantum mechanics is the existence of entangled states. We propose a realistic scenario making it possible to detect entanglement of a mechanical resonator and a qubit in a nanoelectromechanical setup. The detection scheme involves only standard current and noise measurements of an atomic point contact coupled to an oscillator and a qubit. This setup could allow for the first observation of entanglement between a continuous and a discrete quantum system in the solid state.

Using Josephson junctions to determine the pairing state of superconductors without crystal inversion symmetry

Using Josephson junctions to determine the pairing state of superconductors without crystal inversion symmetry

Scheme for steady-state preparation of a harmonic oscillator in the first excited state

We present a generic quantum master equation whose dissipative dynamics autonomously stabilizes a harmonic oscillator in the n=1 Fock state. A multi-mode optomechanical system is analyzed and shown to be an example of a physical system obeying this model. We show that the optomechanical setup enables preparation of a mechanical oscillator in a nonclassical steady state, and that this state indeed approaches a single phonon Fock state in the ideal parameter regime. The generic model may be useful in other settings, such as cavity or circuit quantum electrodynamics or trapped ion physics.