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

Feedback control of probability amplitudes for two-level atom in optical field

We demonstrate the possibility to stabilize the probability amplitude of the upper level for a single quantum two-level atom in a classical optical field with feedback control scheme.Comment: 7 pages, 3 figure

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

Directly Observing Momentum Transfer in Twin-Slit "Which-Way" Experiments

Is the destruction of interference by a which-way measurement due to a random momentum transfer \wp\agt\hbar/s, with $s$ the slit separation? The weak-valued probability distribution $P_{\rm wv}(\wp)$, which is {\em directly observable}, provides a subtle answer. $P_{\rm wv}(\wp)$ cannot have support on the interval $[-\hbar/s,\hbar/s]$. Nevertheless, its moments can be identically zero.Comment: 5 pages, 1 figure. Almost the version almost accepted for publication in Phys. Lett.

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

A partition of connected graphs

We define an algorithm k which takes a connected graph G on a totally ordered vertex set and returns an increasing tree R (which is not necessarily a subtree of G). We characterize the set of graphs G such that k(G)=R. Because this set has a simple structure (it is isomorphic to a product of non-empty power sets), it is easy to evaluate certain graph invariants in terms of increasing trees. In particular, we prove that, up to sign, the coefficient of x^q in the chromatic polynomial of G is the number of increasing forests with q components that satisfy a condition that we call G-connectedness. We also find a bijection between increasing G-connected trees and broken circuit free subtrees of G.Comment: 8 page

Enumeration of paths and cycles and e-coefficients of incomparability graphs

We prove that the number of Hamiltonian paths on the complement of an acyclic digraph is equal to the number of cycle covers. As an application, we obtain a new expansion of the chromatic symmetric function of incomparability graphs in terms of elementary symmetric functions. Analysis of some of the combinatorial implications of this expansion leads to three bijections involving acyclic orientations