Session B4: Hybrid Systems, Optomechanics and Macroscopic Systems at the Quantum Limit I

Observing quantum phenomena in cavity optomechanics

Recent efforts have produced optomechanical systems whose mechanical elements are prepared at or near their quantum ground state. But what manifestly quantum effects can be measured with these new systems? Here we present results from our experiment, using the collective motion of an ultracold atom ensemble as a mechanical oscillator. The motion is driven by shot noise in the light's radiation pressure, allowing us to observe the production of nonclassical states of light by optomechanics -- here, quadrature-squeezed light. Notably, this nonlinear optical effect occurs with only 40 pW of pump power. We also measure the quantization of the oscillator, by observing a 3:1 asymmetry in the light it scatters to low- and high-energy optical sidebands. Analyzing the light emitted from the cavity moreover provides a spectroscopic record of the energy exchanged between light and motion, allowing us to directly quantify the necessary diffusive heating of a quantum backaction-limited position measurement.   

Cryogenic optomechanics with a 261kHz mechanical oscillator

Mechanical motion can interact with light via radiation pressure force. With recent experimental advances over the last few years, such optomechanical coupling has been used to reach quantum ground state of mechanical oscillators, which opens interesting new regime of observing quantum mechanics in macroscopic objects. The optomechanical devices used in this talk consist of a dielectric SiN membrane located inside a high finesse optical cavity. Combining cryogenic cooling in He3 refrigerator and resolved sideband laser cooling enables us to cool the membrane's mechanical mode (whose mechanical frequency is 261kHz) to less than 60 phonons. We will describe some technical challenges in our experiments such as the role of classical phase noise of the cooling laser at the mechanical frequency and our efforts to significantly reduce it via a filter cavity.~   

Ultraefficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control

There is presently a great deal of interest in cooling high-frequency micro- and nano-mechanical oscillators to their ground states. The present state of the art in cooling mechanical resonators is a version of sideband cooling, which was originally developed in the context of cooling trapped ions. Here we present a method based on quantum control that uses the same configuration as sideband cooling--coupling the resonator to be cooled to a second microwave (or optical) auxiliary resonator--but will cool significantly colder. This is achieved by applying optimal control and varying the strength of the coupling between the two resonators over a time on the order of the period of the mechanical resonator. As part of our analysis, we also obtain a method for fast, high-fidelity quantum information transfer between resonators.   

Postselected optomechanical superpositions

We present a scheme for achieving macroscopic quantum superpositions in weakly coupled optomechanical systems by using single photon postselection. This method allows the creation of macroscopic superpositions with currently achievable device parameters, and allows observation of decoherence on a timescale unconstrained by the system's optical decay time. This method relieves many of the challenges associated with previous optical schemes for measuring macroscopic superpositions, and only requires the devices to be in the weak coupling regime. Prospects for observing novel decoherence mechanisms are also discussed.   

Coupling a single spin in diamond to the quantum motion of a mechanical cantilever

We present theoretical considerations for a magnetized mechanical cantilever coupled to a single electronic spin associated with a nitrogen-vacancy (NV) defect center in diamond. This coupled system has recently been implemented in an experiment where the NV spin was used to detect the thermal motion of a magnetic force microscope cantilever at room temperature, reading out the spin state optically using the spin-selective fluorescence of the NV. The possibility to extend this system to the quantum regime opens the door to applications such as readout and transfer of quantum information, as well as interesting theoretical questions. For example, it should be possible to reach the regime of strong coupling between the spin and the motion of the cantilever, in analogy to cavity quantum electrodynamics. We discuss the prospects for reaching the strong coupling regime and the conditions for measuring the onset of quantum effects, such as measuring the zero point motion of the cantilever using the spin as a detector.   

Thermally induced parametric instability in back-action evading measurement of micromechanical quadrature near the zero-point level

Back-action evading (BAE) measurement of mechanical resonators allows, in principle, detection of a single quadrature of motion with sensitivity far below the standard quantum limit, limited in practice only by the non-idealities in the measurement. We report the results of experiments utilizing two-tone BAE in a tightly coupled cavity quantum electro-mechanical system ($\omega_c$=7.1GHz, $\omega_m$=10MHz, g=14MHz/nm). Due to excess dissipation in the microwave cavity, we observe a parametric instability induced by the thermal shift of mechanical resonance frequency. This bounds the minimum position imprecision on one quadrature and we measure the imprecision reaching twice the zero-point motion. We discuss the device requirements to avoid this thermal mechanism and perform measurements below the zero-point level.   

Mechanical squeezing via parametric amplification and feedback control

We discuss the mechanical squeezing that can result from position measurement and feedback applied to a parametrically driven mechanical oscillator. If the parametric drive is optimally detuned from resonance, correlations between the quadratures of motion allow unlimited steady-state squeezing. This contrasts to a parametric drive alone, which is limited to 3dB of squeezing. Compared to back-action evasion, we demonstrate that the measurement strength, temperature and efficiency requirements for quantum squeezing are significantly relaxed.   

Asymmetric absorption and emission of energy by a macroscopic mechanical oscillator in a microwave circuit optomechanical system

We measure the asymmetry in rates for emission and absorption of mechanical energy in an electromechanical system composed of a macroscopic suspended membrane coupled to a high-Q, superconducting microwave resonant circuit. This asymmetry is inherently quantum mechanical because it arises from the inability to annihilate the mechanical ground state. As such, it is only appreciable when the average mechanical occupancy approaches one. This measurement is now possible due to the recent achievement of ground state cooling of macroscopic mechanical oscillators [1,2]. Crucially, we measure the thermal cavity photon occupancy and account for it in our analysis. Failure to correctly account for the interference of these thermal photons with the mechanical signal can lead to a misinterpretation of the data and an overestimate of the emission/absorption asymmetry. \\[4pt] [1] J. D. Teufel, T. Donner, Dale Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, R. W. Simmonds, ``Sideband Cooling Micromechanical Motion to the Quantum Ground State,'' Nature, 475, 359–363 (2011).\\[0pt] [2] Jasper Chan, et al, ``Laser cooling of a nanomechanical oscillator into its quantum ground state,'' Nature, 478, 89-92 (2011).   

Quantum many-body system based on phonons and donors in silicon

Cold atoms in optical lattices have become an indispensable tool for the study of many-body physics. Here, we introduce a novel many-body quantum system based on phonons with potentially useful properties. Theoretical results will be presented on the possibility of interacting systems based on phonitons, hybrid composite objects of a matter excitation and a cavity phonon. We discuss experimentally accessible regimes in silicon phoniton systems involving Mott insulator and superfluid phases. We consider experimental tools to probe these many-body states and give explicit designs for devices where they can be observed.   

Development of a dispersive read-out technique for quantum measurements of nanomechanical resonators

The development of techniques to observe non-classical behavior of micro- and nano- scale mechanical structures has received considerable attention in recent years because of the potential to use these systems for fundamental studies of quantum mechanics as well as their possible role as new technologies for applications ranging from the sensing of weak forces to quantum communication. One important route for observing such behavior is the coupling of micro- and nanomechanical resonators with superconducting qubits. Under certain conditions, qubit-coupled mechanical devices are formally analogous to Jaynes-Cummings systems which have been used in fields such as cavity QED for explorations of matter-radiation interactions and the quantum nature of light. Correspondingly, experiments in the last couple of years have begun to develop superconducting qubits as tools to manipulate and measure quantum states of mechanics. In this talk, we will discuss our efforts to integrate charge-type superconducting qubits as elements for dispersive (non-resonant) read-out and control of nanomechanical resonators, including preliminary system design and the prospects of implementing this system for read-out of the number-state statistics of nanomechanical modes.   

Measuring Quantum Optomechanical Self-induced Oscillations: Photon Correlation and Homodyne Tomography

Motivated by recent experimental advances in fabricating systems with large optomechanical couplings, we study the self-induced mechanical oscillations in the strong quantum regime for a single cell optomechanical system. We show that, under strong optomechanical coupling $g_M\ge\kappa$, the \emph{persistent }state of the mechanical oscillator can have non-classical, \emph{strongly negative} Wigner density, which can be measured by non-destructive homodyne tomography. We further propose to detect the onset of the quantum self-induced oscillation using the easier-to-measure photon two-point correlation functions $g^{(2)}(t)$. We show that there are two distinct signatures in the long-term time-average and the line-shape of $g^{(2)}(t)$ at the onset of self-induced oscillations. We show that $g^{(2)}(t)$ exhibits long-term coherence extending much beyond the optical decay time $1/\kappa$, the decay of which in the red- and blue-detune regime we explain using models of optomechanical cooling and phase noise.   

Controllable Coherent Transfer between a Superconducting Resonator and a Mechanical Oscillator

We report experimental results of controllable coupling between a 7.5 GHz superconducting resonator and a 10 MHz mechanical oscillator. Through time domain measurements, we demonstrate controlled coherent energy transfer between these two systems. Furthermore, by utilizing a Josephson parametric amplifier we have been able to verify coherent transfer of small amplitude states. We compare these results to frequency domain measurements and discuss experimental limitations.   

Using interference for high fidelity quantum state transfer in optomechanics

We present a theoretical study of a two-cavity optomechanical system (e.g. a single mechanical resonator coupled to both a microwave and an optical cavity), investigating how interference can be used to perform mechanically-mediated quantum state transfer between the two cavities. We show that this optomechanical system possesses an effective ``mechanically-dark'' mode which is immune to mechanical dissipation; utilizing this feature allows highly efficient transfer of intra-cavity states, as well as of itinerant photon states. Simple analytic expressions for the fidelity of transferring both Gaussian and non-Gaussian states are provided. Our work has relevance to ongoing experimental efforts in quantum optomechanics (e.g., C.~A.~Regal and K.~W.~Lehnert, J. Phys.: Conf. Ser. 264, 012025 (2011); A.~H.~Safavi-Naeini and O.~Painter, New J. Phys. 13, 013017 (2011)).   

Adiabatic State Conversion and Photon Transmission in Optomechanical Systems

Light-matter interaction in optomechanical systems in the strong coupling regime can be explored as a tool to transfer cavity states and to transmit photon pulses. Here, we show that quantum state conversion between cavity modes with different wavelengths can be realized with high fidelity by adiabatically varying the effective optomechanical couplings. During this adiabatic process, the quantum state is preserved in the dark mode of the cavities, similar to the adiabatic transfer schemes in EIT systems. The fidelity for gaussian states is derived by solving the Langevin equation in the adiabatic limit and shows negligible dependence on the mechanical noise. We also show that an input pulse can be transmitted to an output channel with a different wavelength via the effective optomechanical couplings. The condition for optimal transmission is derived in the frequency domain. Input pulses with a narrow spectral width can be transmitted with high fidelity. For input pulses with a large spectral width, the shape of the output pulses can be manipulated by applying time-dependent effective couplings. (1) L. Tian, arXiv:1111.2119. (2) L. Tian and H. L. Wang, Phys. Rev. A 82, 053806 (2010).   

Single atom array to form a Rydberg ring

Single atom arrays are ideal quantum systems for studying few-body quantum simulation and quantum computation [1]. Towards realizing a fully controllable array we did a lot of experimental efforts, which include rotating single atoms in a ring optical lattice generated by a spatial light modulator [2], high efficient loading of two atoms into a microscopic optical trap by dynamically reshaping the trap with a spatial light modulator [3], and trapping a single atom in a blue detuned optical bottle beam trap [4]. Recently, we succeeded in trapping up to 6 atoms in a ring optical lattice with one atom in each site. Further laser cooling the array and manipulation of the inner states will provide chance to form Ryberg rings for quantum simulation. \\[4pt] [1] M. Saffman et al., Rev. Mod. Phys. 82, 2313 (2010)\\[0pt] [2] X.D. He et al., Opt. Express 17, 21014 (2009)\\[0pt] [3] X.D. He et al., Opt. Express 18, 13586 (2010)\\[0pt] [4] P. Xu et al., Opt. Lett. 35, 2164 (2010)