Single microwave photon detection in the micromaser

High efficiency single photon detection is an interesting problem for many areas of physics, including low temperature measurement, quantum information science and particle physics. For optical photons, there are many examples of devices capable of detecting single photons with high efficiency. However reliable single photon detection of microwaves is very difficult, principally due to their low energy. In this paper we present the theory of a cascade amplifier operating in the microwave regime that has an optimal quantum efficiency of 93%. The device uses a microwave photon to trigger the stimulated emission of a sequence of atoms where the energy transition is readily detectable. A detailed description of the detector's operation and some discussion of the potential limitations of the detector are presented.Comment: 8 pages, 5 figure

Dyck Paths, Motzkin Paths and Traffic Jams

It has recently been observed that the normalization of a one-dimensional out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random sequential dynamics, is exactly equivalent to the partition function of a two-dimensional lattice path model of one-transit walks, or equivalently Dyck paths. This explains the applicability of the Lee-Yang theory of partition function zeros to the ASEP normalization. In this paper we consider the exact solution of the parallel-update ASEP, a special case of the Nagel-Schreckenberg model for traffic flow, in which the ASEP phase transitions can be intepreted as jamming transitions, and find that Lee-Yang theory still applies. We show that the parallel-update ASEP normalization can be expressed as one of several equivalent two-dimensional lattice path problems involving weighted Dyck or Motzkin paths. We introduce the notion of thermodynamic equivalence for such paths and show that the robustness of the general form of the ASEP phase diagram under various update dynamics is a consequence of this thermodynamic equivalence.Comment: Version accepted for publicatio

The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk

The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for nonequilibrium dynamics, in particular driven diffusive processes. It is usually considered in a canonical ensemble in which the number of sites is fixed. We observe that the grand-canonical partition function for the ASEP is remarkably simple. It allows a simple direct derivation of the asymptotics of the canonical normalization in various phases and of the correspondence with One-Transit Walks recently observed by Brak et.al.Comment: Published versio

Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses

Metastable states in Ising spin-glass models are studied by finding iterative solutions of mean-field equations for the local magnetizations. Two different equations are studied: the TAP equations which are exact for the SK model, and the simpler `naive-mean-field' (NMF) equations. The free-energy landscapes that emerge are very different. For the TAP equations, the numerical studies confirm the analytical results of Aspelmeier et al., which predict that TAP states consist of close pairs of minima and index-one (one unstable direction) saddle points, while for the NMF equations saddle points with large indices are found. For TAP the barrier height between a minimum and its nearby saddle point scales as (f-f_0)^{-1/3} where f is the free energy per spin of the solution and f_0 is the equilibrium free energy per spin. This means that for `pure states', for which f-f_0 is of order 1/N, the barriers scale as N^{1/3}, but between states for which f-f_0 is of order one the barriers are finite and also small so such metastable states will be of limited physical significance. For the NMF equations there are saddles of index K and we can demonstrate that their complexity Sigma_K scales as a function of K/N. We have also employed an iterative scheme with a free parameter that can be adjusted to bring the system of equations close to the `edge of chaos'. Both for the TAP and NME equations it is possible with this approach to find metastable states whose free energy per spin is close to f_0. As N increases, it becomes harder and harder to find solutions near the edge of chaos, but nevertheless the results which can be obtained are competitive with those achieved by more time-consuming computing methods and suggest that this method may be of general utility.Comment: 13 page

An introduction to phase transitions in stochastic dynamical systems

We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much as possible to discuss both cases within the same conceptual framework, focussing on dynamically attractive `peaks' in state space. A quantitative characterisation of these peaks leads to expressions for the partition function and free energy that extend from equilibrium steady states to their nonequilibrium counterparts. We show that for certain classes of nonequilibrium systems that have been exactly solved, these expressions provide precise predictions of their macroscopic phase behaviour.Comment: Pedagogical talk contributed to the "Ageing and the Glass Transition" Summer School, Luxembourg, September 2005. 12 pages, 8 figures, uses the IOP 'jpconf' document clas

Carrier-induced ferromagnetism in n-type ZnMnAlO and ZnCoAlO thin films at room temperature

The realization of semiconductors that are ferromagnetic above room temperature will potentially lead to a new generation of spintronic devices with revolutionary electrical and optical properties. Transition temperatures in doped ZnO are high but, particularly for Mn doping, the reported moments have been small. We show that by careful control of both oxygen deficiency and aluminium doping the ferromagnetic moments measured at room temperature in n-type ZnMnO and ZnCoO are close to the ideal values of 5mB and 3mB respectively. Furthermore a clear correlation between the magnetisation per transition metal ion and the ratio of the number of carriers to the number of transition metal donors was established as is expected for carrier induced ferromagnetism for both the Mn and Co doped films. The dependence of the magnetisation on carrier density is similar to that predicted for the transition temperature for a dilute magnetic semiconductor in which the exchange between the transition metal ions is through the free carriers.Comment: 14 pages pd

Spatiotemporally Complete Condensation in a Non-Poissonian Exclusion Process

We investigate a non-Poissonian version of the asymmetric simple exclusion process, motivated by the observation that coarse-graining the interactions between particles in complex systems generically leads to a stochastic process with a non-Markovian (history-dependent) character. We characterize a large family of one-dimensional hopping processes using a waiting-time distribution for individual particle hops. We find that when its variance is infinite, a real-space condensate forms that is complete in space (involves all particles) and time (exists at almost any given instant) in the thermodynamic limit. The mechanism for the onset and stability of the condensate are both rather subtle, and depends on the microscopic dynamics subsequent to a failed particle hop attempts.Comment: 5 pages, 5 figures. Version 2 to appear in PR

Perturbation theory for the one-dimensional trapping reaction

We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a perturbation series expansion in the diffusion constant of the particle. We calculate the persistence exponent associated with the particle's survival probability to second order and find that it is characterised by the asymmetry in the number of traps initially positioned on each side of the particle.Comment: 18 pages, no figures. Uses IOP Latex clas

Magnetic and Optical properties of strained films of multiferroic GdMnO3

The effects of strain on a film of mulitferroic GdMnO3 are investigated using both magnetometry and magneto-optic spectroscopy. Optical spectra, in the energy range 1.5eV - 3.5eV, were taken in Faraday geometry in an applied magnetic field and also at remanence. This yielded rich information on the effects of strain on the spin ordering in these films. Epitaxial films of GdMnO3 were grown on SrTiO3 and LaAlO3 substrates. The LaAlO3 was twinned and so produced a highly strained film whereas the strain was less for the film grown on SrTiO3. The Ne\'el temperatures and coercive fields were measured using zero field data and hysteresis loops obtained using a SQUID magnetometer. Optical absorption data agreed with earlier work on bulk materials. The two well known features in the optical spectrum, the charge transfer transition between Mn d states at ~2eV and the band edge transition from the oxygen p band to the d states at ~3eV are observed in the magnetic circular dichroism; however they behaved very differently both as a function of magnetic field and temperature. This is interpreted in terms of the magnetic ordering of the Mn spins.Comment: 9 pages of text including figure