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Register a new userCooling of mechanical motion with a two level system: the high temperature regime
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P. Rabl
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We analyze cooling of a nano-mechanical resonator coupled to a dissipative solid state two level system focusing on the regime of high initial temperatures. We derive an effective Fokker-Planck equation for the mechanical mode which accounts for saturation and other non-linear effects and allows us to study the cooling dynamics of the resonator mode for arbitrary occupation numbers. We find a degrading of the cooling rates and eventually a breakdown of cooling at very high initial temperatures and discuss the dependence of these effects on various system parameters. Our results apply to most solid state systems which have been proposed for cooling a mechanical resonator including quantum dots, superconducting qubits and electronic spin qubits.
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Coupling electromagnetic waves in a cavity and mechanical vibrations via the radiation pressure of the photons [1,2] is a promising platform for investigations of quantum mechanical properties of motion of macroscopic bodies and thereby the limits of quantum mechanics [3,4]. A drawback is that the effect of one photon tends to be tiny, and hence one of the pressing challenges is to substantially increase the interaction strength towards the scale of the cavity damping rate. A novel scenario is to introduce into the setup a quantum two-level system (qubit), which, besides strengthening the coupling, allows for rich physics via strongly enhanced nonlinearities [5-8]. Addressing these issues, here we present a design of cavity optomechanics in the microwave frequency regime involving a Josephson junction qubit. We demonstrate boosting of the radiation pressure interaction energy by six orders of magnitude, allowing to approach the strong coupling regime, where a single quantum of vibrations shifts the cavity frequency by more than its linewidth. We observe nonlinear phenomena at single-photon energies, such as an enhanced damping due to the two-level system. This work opens up nonlinear cavity optomechanics as a plausible tool for the study of quantum properties of motion.
We present a single-quadrature feedback scheme able to overcome the conventional 3 dB limit on parametric squeezing. The method is experimentally demonstrated in a micromechanical system based on a cantilever with a magnetic tip. The cantilever is detected at low temperature by a SQUID susceptometer, while parametric pumping is obtained by modulating the magnetic field gradient at twice the cantilever frequency. A maximum squeezing of 11.5 dB and 11.3 dB is observed, respectively in the response to a sinusoidal test signal and in the thermomechanical noise. The maximum squeezing factor is limited only by the maximum achievable parametric modulation. The proposed technique can be used to squeeze one quadrature of a mechanical resonator below the quantum noise level, even without the need for a quantum limited detector.
A quantum theory of cooling of a mechanical oscillator by radiation pressure-induced dynamical back-action is developed, which is analogous to sideband cooling of trapped ions. We find that final occupancies well below unity can be attained when the mechanical oscillation frequency is larger than the cavity linewidth. It is shown that the final average occupancy can be retrieved directly from the optical output spectrum.
In quantum physics, two prototypical model systems stand out due to their wide range of applications. These are the two-level system (TLS) and the harmonic oscillator. The former is often an ideal model for confined charge or spin systems and the latter for lattice vibrations, i.e., phonons. Here, we couple these two systems, which leads to numerous fascinating physical phenomena. Practically, we consider different optical excitations and decay scenarios of a TLS, focusing on the generated dynamics of a single phonon mode that couples to the TLS. Special emphasis is placed on the entropy of the different parts of the system, predominantly the phonons. While, without any decay, the entire system is always in a pure state, resulting in a vanishing entropy, the complex interplay between the single parts results in non-vanishing respective entanglement entropies and non-trivial dynamics of them. Taking a decay of the TLS into account leads to a non-vanishing entropy of the full system and additional aspects in its dynamics. We demonstrate that all aspects of the entropys behavior can be traced back to the purity of the states and are illustrated by phonon Wigner functions in phase space.
A superconducting qubit was driven in an ultrastrong fashion by an oscillatory microwave field, which was created by coupling via the nonlinear Josephson energy. The observed Stark shifts of the `atomic levels are so pronounced that corrections even beyond the lowest-order Bloch-Siegert shift are needed to properly explain the measurements. The quasienergies of the dressed two-level system were probed by resonant absorption via a cavity, and the results are in agreement with a calculation based on the Floquet approach.
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