Complete parameterization, and invariance, of diffusive quantum trajectories for Markovian open systems

The state matrix $\rho$ for an open quantum system with Markovian evolution obeys a master equation. The master equation evolution can be unraveled into stochastic nonlinear trajectories for a pure state $P$, such that on average $P$ reproduces $\rho$. Here we give for the first time a complete parameterization of all diffusive unravelings (in which $P$ evolves continuously but non-differentiably in time). We give an explicit measurement theory interpretation for these quantum trajectories, in terms of monitoring the system's environment. We also introduce new classes of diffusive unravelings that are invariant under the linear operator transformations under which the master equation is invariant. We illustrate these invariant unravelings by numerical simulations. Finally, we discuss generalized gauge transformations as a method of connecting apparently disparate descriptions of the same trajectories by stochastic Schr\"odinger equations, and their invariance properties.Comment: 10 pages, including 5 figures, submitted to J. Chem Phys special issue on open quantum system

Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment

Quantum feedback can stabilize a two-level atom against decoherence (spontaneous emission), putting it into an arbitrary (specified) pure state. This requires perfect homodyne detection of the atomic emission, and instantaneous feedback. Inefficient detection was considered previously by two of us. Here we allow for a non-zero delay time $\tau$ in the feedback circuit. Because a two-level atom is a nonlinear optical system, an analytical solution is not possible. However, quantum trajectories allow a simple numerical simulation of the resulting non-Markovian process. We find the effect of the time delay to be qualitatively similar to that of inefficient detection. The solution of the non-Markovian quantum trajectory will not remain fixed, so that the time-averaged state will be mixed, not pure. In the case where one tries to stabilize the atom in the excited state, an approximate analytical solution to the quantum trajectory is possible. The result, that the purity ($P=2{\rm Tr}[\rho^{2}]-1$) of the average state is given by $P=1-4\gamma\tau$ (where $\gamma$ is the spontaneous emission rate) is found to agree very well with the numerical results.Comment: Changed content, Added references and Corrected typo

On black hole thermodynamics from super Yang-Mills

We consider maximally supersymmetric U(N) Yang-Mills in (1+p)-dimensions for p < 3. In the 't Hooft large N limit this is conjectured to be dual to N Dp-branes in the decoupling limit. At low temperatures T << \lambda^{1/(3-p)} governed by the dimensionful 't Hooft coupling \lambda, supergravity black holes predict the free energy density goes as ~ N^2 T^{2(7-p)/(5-p)} and the expectation value of the scalars goes as ~ T^{2/(5-p)}, with dimensions made up by \lambda. The purpose of this work is to explain the origin of these peculiar powers of temperature. We argue that these powers naturally arise by requiring that the low energy moduli of the theory become strongly coupled at low temperature. As an application, we consider the BMN quantum mechanics that results from a supersymmetric deformation of the p=0 theory. The black holes dual to this deformed theory have not yet been constructed, and our analysis can be used to make an explicit prediction for their thermodynamic behaviour.Comment: 28 pages, no figures. v2: journal version - minor corrections, references adde

A New Materialism: A Reading of the New Art from China

This essay has three parts. The first moves from what artists confronted when China was first opened to the west in 1978 to what two classical Chinese critics and artists said art was and how it was to be made. The second looks at artists’ works made between two exhibitions in the United States, one in 1998, the other in 2017, to find an uncanny reprise of the classical principles. The third looks at the ideas of the global, contemporary, and art through the works of Peter Osborne and Arthur Danto that apply to the new art from China

A low energy rare event search with the MAJORANA DEMONSTRATOR

Abstract The MAJORANA DEMONSTRATOR is sensitive to rare events near its energy threshold, including bosonic dark matter, solar axions, and lightly ionizing particles. In this analysis, a novel training set of low energy small-angle Compton scatter events is used to determine the efficiency of pulse shape analysis cuts, and we present updated bosonic dark matter and solar axion results from an 11.17 kg-y dataset using a 5 keV analysis threshold

Adaptive Quantum Measurements of a Continuously Varying Phase

We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both non-adaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be \dot\phi = \sqrt{\kappa}\xi(t), where \xi(t) is \delta-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/\hbar\omega\kappa, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance \simeq N^{-1/2}/2. This is \sqrt{2} times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as N^{-2/3}, compared to N^{-1/2} for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as N^{-1/2}. It offers a significant improvement over nonadaptive interferometry only for N of order unity.Comment: 11 pages, 6 figures, journal versio