Non-equilibrium properties of trapped ions under sudden application of a laser

Coherent quantum-state manipulation of trapped ions using classical laser fields is a trademark of modern quantum technologies. In this work, we study aspects of work statistics and irreversibility in a single trapped ion due to sudden interaction with the impinging laser. This is clearly an out-of-equilibrium process where work is performed through illumination of an ion by the laser. Starting with the explicit evaluation of the first moments of the work distribution, we proceed to a careful analysis of irreversibility as quantified by the nonequilibrium lag. The treatment employed here is not restricted to the Lamb-Dicke limit, what allows us to investigate the interplay between nonlinearities and irreversibility. We show, for instance, that in the resolved carrier and sideband regimes, variation of the Lamb-Dicke parameter may cause a non-monotonic behavior of the irreversibility indicator. Counterintuitively, we find a working point where nonlinearity helps reversibility, making the sudden quench of the Hamiltonian closer to what would have been obtained quasistatically and isothermally.

Non-equilibrium thermodynamics of harmonically trapped bosons

We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-size bosonic quantum gases in a harmonic trap. By studying the temporal behaviour of the Loschmidt echo and of the atomic density profile within the trap, which are informative of the non-equilibrium physics and the correlations among the particles, we establish a link with the statistics of (irreversible) work done on the system. This highlights interesting connections between the degree of inter-particle entanglement and the non-equilibrium thermodynamics of the system.

Formation of helical ion chains

We study the nonequilibrium dynamics of the linear to zigzag structural phase transition exhibited by an ion chain confined in a trap with periodic boundary conditions. The transition is driven by reducing the transverse confinement at a finite quench rate, which can be accurately controlled. This results in the formation of zigzag domains oriented along different transverse planes. The twists between different domains can be stabilized by the topology of the trap and under laser cooling the system has a chance to relax to a helical chain with nonzero winding number. Molecular dynamics simulations are used to obtain a large sample of possible trajectories for different quench rates. The scaling of the average winding number with different quench rates is compared to the prediction of the Kibble-Zurek theory, and a good quantitative agreement is found.

Hydrodynamics of domain walls in ferroelectrics and multiferroics: Impact on memory devices

The standard “Kittel Law” for the thickness and shape of ferroelectric, ferroelastic, or ferromagnet domains assumes mechanical equilibrium. The present paper shows that such domains may be highly nonequilibrium, with unusual thicknesses and shapes. In lead germanate and multiferroic lead zirconate titanate iron tantalate domain wall instabilities resemble hydrodynamics (Richtmyer–Meshkov and Helfrich–Hurault, respectively).

Constant wall heat flux boundary conditions in micro-channels filled with porous material with internal heat generation under local thermal non-equilibrium conditions

Forced convection heat transfer in a micro-channel filled with a porous material saturated with rarefied gas with internal heat generation is studied analytically in this work. The study is performed by analysing the boundary conditions for constant wall heat flux under local thermal non-equilibrium (LTNE) conditions. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous-fluid system is studied by considering thermally and hydrodynamically fully-developed conditions. The flow inside the porous material is modelled by the Darcy–Brinkman equation. Exact solutions are obtained for both the fluid and solid temperature distributions for two primary approaches models A and B using constant wall heat flux boundary conditions. The temperature distributions and Nusselt numbers for models A and B are compared, and the limiting cases resulting in the convergence or divergence of the two models are also discussed. The effects of pertinent parameters such as fluid to solid effective thermal conductivity ratio, Biot number, Darcy number, velocity slip and temperature jump coefficients, and fluid and solid internal heat generations are also discussed. The results indicate that the Nusselt number decreases with the increase of thermal conductivity ratio for both models. This contrasts results from previous studies which for model A reported that the Nusselt number increases with the increase of thermal conductivity ratio. The Biot number and thermal conductivity ratio are found to have substantial effects on the role of temperature jump coefficient in controlling the Nusselt number for models A and B. The Nusselt numbers calculated using model A change drastically with the variation of solid internal heat generation. In contrast, the Nusselt numbers obtained for model B show a weak dependency on the variation of internal heat generation. The velocity slip coefficient has no noticeable effect on the Nusselt numbers for both models. The difference between the Nusselt numbers calculated using the two models decreases with an increase of the temperature jump coefficient.

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces

Thesis (Ph.D.)--University of Washington, 2016-08

Experimental and analytical investigation of refrigerant and lubricant migration

The off-cycle refrigerant mass migration has a direct influence on the on-cycle performance since compressor energy is necessary to redistribute the refrigerant mass. No studies, as of today, are available in the open literature which experimentally measured the lubricant migration within a refrigeration system during cycling or stop/start transients. Therefore, experimental procedures measuring the refrigerant and lubricant migration through the major components of a refrigeration system during stop/start transients were developed and implemented. Results identifying the underlying physics are presented. The refrigerant and lubricant migration of an R134a automotive A/C system-utilizing a fixed orifice tube, minichannel condenser, plate and fin evaporator, U-tube type accumulator and fixed displacement compressor-was measured across five sections divided by ball valves. Using the Quick-Closing Valve Technique (QCVT) combined with the Remove and Weigh Technique (RWT) using liquid nitrogen as the condensing agent resulted in a measurement uncertainty of 0.4 percent regarding the total refrigerant mass in the system. The determination of the lubricant mass distribution was achieved by employing three different techniques-Remove and Weigh, Mix and Sample, and Flushing. To employ the Mix and Sample Technique a device-called the Mix and Sample Device-was built. A method to separate the refrigerant and lubricant was developed with an accuracy-after separation-of 0.04 grams of refrigerant left in the lubricant. When applying the three techniques, the total amount of lubricant mass in the system was determined to within two percent. The combination of measurement results-infrared photography and high speed and real time videography-provide unprecedented insight into the mechanisms of refrigerant and lubricant migration during stop-start operation. During the compressor stop period, the primary refrigerant mass migration is caused by, and follows, the diminishing pressure difference across the expansion device. The secondary refrigerant migration is caused by a pressure gradient as a result of thermal nonequilibrium within the system and causes only vapor phase refrigerant migration. Lubricant migration is proportional to the refrigerant mass during the primary refrigerant mass migration. During the secondary refrigerant mass migration lubricant is not migrating. The start-up refrigerant mass migration is caused by an imbalance of the refrigerant mass flow rates across the compressor and expansion device. The higher compressor refrigerant mass flow rate was a result of the entrainment of foam into the U-tube of the accumulator. The lubricant mass migration during the start-up was not proportional to the refrigerant mass migration. The presence of water condensate on the evaporator affected the refrigerant mass migration during the compressor stop period. Caused by an evaporative cooling effect the evaporator held 56 percent of the total refrigerant mass in the system after three minutes of compressor stop time-compared to 25 percent when no water condensate was present on the evaporator coil. Foam entrainment led to a faster lubricant and refrigerant mass migration out of the accumulator than liquid entrainment through the hole at the bottom of the U-tube. The latter was observed for when water condensate was present on the evaporator coil because-as a result of the higher amount of refrigerant mass in the evaporator before start-up-the entrainment of foam into the U-tube of the accumulator ceased before the steady state refrigerant mass distribution was reached.

Superconducting Transition-Edge Sensor Physics

Despite record-setting performance demonstrated by superconducting Transition Edge Sensors (TESs) and growing utilization of the technology, a theoretical model of the physics governing TES devices superconducting phase transition has proven elusive. Earlier attempts to describe TESs assumed them to be uniform superconductors. Sadleir et al. 2010 shows that TESs are weak links and that the superconducting order parameter strength has significant spatial variation. Measurements are presented of the temperature T and magnetic field B dependence of the critical current Ic measured over 7 orders of magnitude on square Mo/Au bilayers ranging in length from 8 to 290 microns. We find our measurements have a natural explanation in terms of a spatially varying order parameter that is enhanced in proximity to the higher transition temperature superconducting leads (the longitudinal proximity effect) and suppressed in proximity to the added normal metal structures (the lateral inverse proximity effect). These in-plane proximity effects and scaling relations are observed over unprecedentedly long lengths (in excess of 1000 times the mean free path) and explained in terms of a Ginzburg-Landau model. Our low temperature Ic(B) measurements are found to agree with a general derivation of a superconducting strip with an edge or geometric barrier to vortex entry and we also derive two conditions that lead to Ic rectification. At high temperatures the Ic(B) exhibits distinct Josephson effect behavior over long length scales and following functional dependences not previously reported. We also investigate how film stress changes the transition, explain some transition features in terms of a nonequilibrium superconductivity effect, and show that our measurements of the resistive transition are not consistent with a percolating resistor network model.

Entropy, chaos, and excited-state quantum phase transitions in the Dicke model

We study nonequilibrium processes in an isolated quantum system-the Dicke model-focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos, and the excited-state quantum phase transition is more clear for the entanglement entropy.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Estudo das propriedades críticas do processo epidêmico por par com difusão de pares

The pair contact process - PCP is a nonequilibrium stochastic model which, like the basic contact process - CP, exhibits a phase transition to an absorbing state. While the absorbing state CP corresponds to a unique configuration (empty lattice), the PCP process infinitely many. Numerical and theoretical studies, nevertheless, indicate that the PCP belongs to the same universality class as the CP (direct percolation class), but with anomalies in the critical spreading dynamics. An infinite number of absorbing configurations arise in the PCP because all process (creation and annihilation) require a nearest-neighbor pair of particles. The diffusive pair contact process - PCPD) was proposed by Grassberger in 1982. But the interest in the problem follows its rediscovery by the Langevin description. On the basis of numerical results and renormalization group arguments, Carlon, Henkel and Schollwöck (2001), suggested that certain critical exponents in the PCPD had values similar to those of the party-conserving - PC class. On the other hand, Hinrichsen (2001), reported simulation results inconsistent with the PC class, and proposed that the PCPD belongs to a new universality class. The controversy regarding the universality of the PCPD remains unresolved. In the PCPD, a nearest-neighbor pair of particles is necessary for the process of creation and annihilation, but the particles to diffuse individually. In this work we study the PCPD with diffusion of pair, in which isolated particles cannot move; a nearest-neighbor pair diffuses as a unit. Using quasistationary simulation, we determined with good precision the critical point and critical exponents for three values of the diffusive probability: D=0.5 and D=0.1. For D=0.5: PC=0.89007(3), β/v=0.252(9), z=1.573(1), =1.10(2), m=1.1758(24). For D=0.1: PC=0.9172(1), β/v=0.252(9), z=1.579(11), =1.11(4), m=1.173(4)