Location- and observation time-dependent quantum-tunneling

We investigate quantum tunneling in a translation invariant chain of particles. The particles interact harmonically with their nearest neighbors, except for one bond, which is anharmonic. It is described by a symmetric double well potential. In the first step, we show how the anharmonic coordinate can be separated from the normal modes. This yields a Lagrangian which has been used to study quantum dissipation. Elimination of the normal modes leads to a nonlocal action of Caldeira-Leggett type. If the anharmonic bond defect is in the bulk, one arrives at Ohmic damping, i.e. there is a transition of a delocalized bond state to a localized one if the elastic constant exceeds a critical value $C_{crit}$. The latter depends on the masses of the bond defect. Superohmic damping occurs if the bond defect is in the site $M$ at a finite distance from one of the chain ends. If the observation time $T$ is smaller than a characteristic time $\tau_M \sim M$, depending on the location M of the defect, the behavior is similar to the bulk situation. However, for $T \gg \tau_M$ tunneling is never suppressed.Comment: 17 pages, 2 figure

Measurement and control of a mechanical oscillator at its thermal decoherence rate

In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen highly successful applications in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. By contrast, the ability to stabilize the quantum state of a tangibly massive object, such as a nanomechanical oscillator, remains a difficult challenge: The main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, nanomechanical oscillator in the timescale of its thermal decoherence, a critical requirement for preparing its ground state using feedback. The sensor is based on cavity optomechanical coupling, and realizes a measurement of the oscillator's displacement with an imprecision 40 dB below that at the standard quantum limit, while maintaining an imprecision-back-action product within a factor of 5 of the Heisenberg uncertainty limit. Using the measurement as an error signal and radiation pressure as an actuator, we demonstrate active feedback cooling (cold-damping) of the 4.3 MHz oscillator from a cryogenic bath temperature of 4.4 K to an effective value of 1.1$\pm$0.1 mK, corresponding to a mean phonon number of 5.3$\pm$0.6 (i.e., a ground state probability of 16%). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of engineered mechanical oscillators as practical subjects for measurement-based quantum control.Comment: 24 pages, 10 figures; typos corrected in main text and figure

Mean-field glass transition in a model liquid

We investigate the liquid-glass phase transition in a system of point-like particles interacting via a finite-range attractive potential in D-dimensional space. The phase transition is driven by an `entropy crisis' where the available phase space volume collapses dramatically at the transition. We describe the general strategy underlying the first-principles replica calculation for this type of transition; its application to our model system then allows for an analytic description of the liquid-glass phase transition within a mean-field approximation, provided the parameters are chosen suitably. We find a transition exhibiting all the features associated with an `entropy crisis', including the characteristic finite jump of the order parameter at the transition while the free energy and its first derivative remain continuous.Comment: 12 pages, 6 figure

Regularization of fluctuations near the sonic horizon due to the quantum potential and its influence on the Hawking radiation

We consider dynamics of fluctuations in transonically accelerating Bose-Einstein condensates and luminous liquids (coherent light propagating in a Kerr nonlinear medium) using the hydrodynamic approach. It is known that neglecting the quantum potential (QP) leads to a singular behavior of quantum and classical fluctuations in the vicinity of the Mach (sonic) horizon, which in turn gives rise to the Hawking radiation. The neglect of QP is well founded at not too small distances $|x| \gg l_h$ from the horizon, where $l_h$ is the healing length. Taking the QP into account we show that a second characteristic length $l_r > l_h$ exists, such that the linear fluctuation modes become regularized for $|x| \ll l_r$. At $|x| \gg l_r$ the modes keep their singular behavior, which however is influenced by the QP. As a result we find a deviation of the high frequency tail of the spectrum of Hawking radiation from Planck's black body radiation distribution. Similar results hold for the wave propagation in Kerr nonlinear media where the length $l_h$ and $l_r$ exist due to the nonlinearity.Comment: 23 pages, 2 figure