Keith Schwab

Self-cooling of a micromirror by radiation pressure.

Cooling of mechanical resonators is currently a popular topic in many fields of physics including ultra-high precision measurements, detection of gravitational waves and the study of the transition between classical and quantum behaviour of a mechanical system. Here we report the observation of self-cooling of a micromirror by radiation pressure inside a high-finesse optical cavity. In essence, changes in intensity in a detuned cavity, as caused by the thermal vibration of the mirror, provide the mechanism for entropy flow from the mirror’s oscillatory motion to the low-entropy cavity field. The crucial coupling between radiation and mechanical motion was made possible by producing free-standing micromirrors of low mass (m ≈ 400 ng), high reflectance (more than 99.6%) and high mechanical quality (Q ≈ 10,000). We observe cooling of the mechanical oscillator by a factor of more than 30; that is, from room temperature to below 10 K. In addition to purely photothermal effects we identify radiation pressure as a relevant mechanism responsible for the cooling. In contrast with earlier experiments, our technique does not need any active feedback. We expect that improvements of our method will permit cooling ratios beyond 1,000 and will thus possibly enable cooling all the way down to the quantum mechanical ground state of the micromirror.

Cooling a nanomechanical resonator with quantum back-action

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radio-frequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latters position; back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK—an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these back-action effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.

Ion trap in a semiconductor chip

The electromagnetic manipulation of isolated atoms has led to many advances in physics, from laser cooling1 and Bose–Einstein condensation of cold gases2 to the precise quantum control of individual atomic ions3. Work on miniaturizing electromagnetic traps to the micrometre scale promises even higher levels of control and reliability4. Compared with ‘chip traps’ for confining neutral atoms5,6,7, ion traps with similar dimensions and power dissipation offer much higher confinement forces and allow unparalleled control at the single-atom level. Moreover, ion microtraps are of great interest in the development of miniature mass-spectrometer arrays8, compact atomic clocks9 and, most notably, large-scale quantum information processors10,11. Here we report the operation of a micrometre-scale ion trap, fabricated on a monolithic chip using semiconductor micro-electromechanical systems (MEMS) technology. We confine, laser cool and measure heating of a single 111Cd+ ion in an integrated radiofrequency trap etched from a doped gallium-arsenide heterostructure.

Dissipation in Nanocrystalline-Diamond Nanomechanical Resonators

We have measured the dissipation and frequency of nanocrystalline-diamond nanomechanical resonators with resonant frequencies between 13.7 MHz and 157.3 MHz, over a temperature range of 1.4–274 K. Using both magnetomotive network analysis and a time-domain ring-down technique, we have found the dissipation in this material to have a temperature dependence roughly following T0.2, with Q−1≈10−4 at low temperatures. The frequency dependence of a large dissipation feature at ∼35–55 K is consistent with thermal activation over a 0.02 eV barrier with an attempt frequency of 10 GHz.

Feedback cooling of a nanomechanical resonator

Cooled, low-loss nanomechanical resonators offer the prospect of directly observing the quantum dynamics of mesoscopic systems. However, the present state of the art requires cooling down to the milliKelvin regime in order to observe quantum effects. Here we present an active feedback strategy based on continuous observation of the resonator position for the purpose of obtaining these low temperatures. In addition, we apply this to an experimentally realizable configuration, where the position monitoring is carried out by a single-electron transistor. Our estimates indicate that with current technology this technique is likely to bring the required low temperatures within reach.

Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator

Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing connections to quantum optics. Several of these experiments address the prototypical problem of cavity quantum electrodynamics: a two-level system coupled to a quantum harmonic oscillator. Such devices may allow the exploration of parameter regimes outside the near-resonance and weak-coupling assumptions of the ubiquitous rotating-wave approximation (RWA), necessitating other theoretical approaches. One such approach is an adiabatic approximation in the limit that the oscillator frequency is much larger than the characteristic frequency of the two-level system. A derivation of the approximation is presented, together with a discussion of its applicability in a system consisting of a Cooper-pair box coupled to a nanomechanical resonator. Within this approximation the time evolution of the two-level-system occupation probability is calculated using both thermal- and coherent-state initial conditions for the oscillator, focusing particularly on collapse and revival phenomena. For thermal-state initial conditions parameter regimes are found in which collapse and revival regions may be clearly distinguished, unlike the erratic evolution of the thermal-state RWA model. Coherent-state initial conditions lead to complex behavior, which exhibits sensitive dependence on the coupling strength and the initial amplitude of the oscillator state. One feature of the regime considered here is that closed-form evaluation of the time evolution may be carried out in the weak-coupling limit, which provides insight into the differences between the thermal- and coherent-state models. Finally, potential experimental observations in solid-state systems, particularly the Cooper-pair box—nanomechanical resonator system, are discussed and found to be promising.

Squeezing of a nanomechanical resonator by quantum nondemolition measurement and feedback

We analyze squeezing of the nanoresonator state produced by periodic measurement of position by a quantum point contact or a single-electron transistor. The mechanism of squeezing is the stroboscopic quantum nondemolition measurement generalized to the case of continuous measurement by a weakly coupled detector. The magnitude of squeezing is calculated for the harmonic and stroboscopic modulations of measurement, taking into account detector efficiency and nanoresonator quality factor. We also analyze the operation of the quantum feedback, which prevents fluctuations of the wave packet center due to measurement back-action. Verification of the squeezed state can be performed in almost the same way as its preparation; a similar procedure can also be used for the force detection with sensitivity beyond the standard quantum limit.

Ion trap transducers for quantum electromechanical oscillators

An enduring challenge for contemporary physics is to experimentally observe and control quantum behavior in macroscopic systems. We show that a single trapped atomic ion could be used to probe the quantum nature of a mesoscopic mechanical oscillator precooled to 4 K, and furthermore, to cool the oscillator with high efficiency to its quantum ground state. The proposed experiment could be performed using currently available technology.

Thermal conductance through discrete quantum channels

We have observed a quantized limiting value of the thermal conductance for each propagating phonon channel in a one-dimensional (1D), ballistic phonon waveguide: g_0=π^2k_B^2T/3h. To achieve this we have developed nanostructures with full three-dimensional relief that incorporate integral thermometers and heaters. These devices are comprised of an isolated thermal reservoir (phonon cavity) suspended above the sample substrate by four narrow insulating beams (phonon waveguides) with lateral dimensions ∼100 nm. We employ DC SQUID noise thermometry to measure the temperature of the phonon cavity non-perturbatively. Direct electrical contact from the suspended nanostructure to the room-temperature environment, crucial for these experiments, is attained by means of a very significant level of electrical filtering. These first experiments provide access to the mesoscopic regime for phonons, and open intriguing future possibilities for exploring thermal transport in very small systems. We are currently adapting and improving the ultrasensitive, extremely low dissipation DC SQUID techniques utilized in this work toward the ultimate goal of detecting individual thermal phonons.

High reflectivity high-Q micromechanical Bragg mirror

The authors report on the fabrication and characterization of a micromechanical oscillator consisting only of a freestanding dielectric Bragg mirror with high optical reflectivity and high mechanical quality. The fabrication technique is a hybrid approach involving laser ablation and dry etching. The mirror has a reflectivity of 99.6%, a mass of 400 ng, and a mechanical quality factor Q of approximately 10^4. Using this micromirror in a Fabry-Perot cavity, a finesse of 500 has been achieved. This is an important step towards designing tunable high-Q high-finesse cavities on chip.