Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Experimental Verification of Decoherence-Free Subspaces

Using spontaneous parametric down-conversion, we produce polarization-entangled states of two photons and characterize them using two-photon tomography to measure the density matrix. A controllable decoherence is imposed on the states by passing the photons through thick, adjustable birefringent elements. When the system is subject to collective decoherence, one particular entangled state is seen to be decoherence-free, as predicted by theory. Such decoherence-free systems may have an important role for the future of quantum computation and information processing.

Fundamental Skills in Physics: Embedded Learning

Student attitudes towards a subject affect their learning. For students in physics service courses, relevance is emphasised by vocational applications. A similar strategy is being used for students who aspire to continued study of physics, in an introduction to fundamental skills in experimental physics – the concepts, computational tools and practical skills involved in appropriately obtaining and interpreting measurement data. An educational module is being developed that aims to enhance the student experience by embedding learning of these skills in the practicing physicist’s activity of doing an experiment (gravity estimation using a rolling pendulum). The group concentrates on particular skills prompted by challenges such as: • How can we get an answer to our question? • How good is our answer? • How can it be improved? This explicitly provides students the opportunity to consider and construct their own ideas. It gives them time to discuss, digest and practise without undue stress, thereby assisting them to internalise core skills. Design of the learning activity is approached in an iterative manner, via theoretical and practical considerations, with input from a range of teaching staff, and subject to trials of prototypes.

Decoherence in ion traps due to laser intensity and phase fluctuations

We consider one source of decoherence for a single trapped ion due to intensity and phase fluctuations in the exciting laser pulses. For simplicity we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. This master equation is averaged over the noise, and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. Our results are in good qualitative agreement with recent experiments and predict that the decoherence rate will depend on vibrational quantum number in different ways depending on which vibrational excitation sideband is used.

Decoherence and fidelity in ion traps with fluctuating trap parameters

We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (wobbling) of the ion relative to the center of the trap, and fluctuations of the spring constant, which an due to fluctuations of the ac component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctuating external electrical fields for a quantum gate operation (controlled-NOT) is determined and the fidelity for that operation derived. [S1050-2947(99)06005-9].

Decoherence and coherent population transfer between two coupled systems

We show that an arbitrary system described by two dipole moments exhibits coherent superpositions of internal states that can be completely decoupled fi om the dissipative interactions (responsible for decoherence) and an external driving laser field. These superpositions, known as dark or trapping states, can he completely stable or can coherently interact with the remaining states. We examine the master equation describing the dissipative evolution of the system and identify conditions for population trapping and also classify processes that can transfer the population to these undriven and nondecaying states. It is shown that coherent transfers are possible only if the two systems are nonidentical, that is the transitions have different frequencies and/or decay rates. in particular, we find that the trapping conditions can involve both coherent and dissipative interactions, and depending on the energy level structure of the system, the population can be trapped in a linear superposition of two or more bare states, a dressed state corresponding to an eigenstate of the system plus external fields or, in some cases. in one of the excited states of the system. A comprehensive analysis is presented of the different processes that are responsible for population trapping, and we illustrate these ideas with three examples of two coupled systems: single V- and Lambda-type three-level atoms and two nonidentical tao-level atoms, which are known to exhibit dark states. We show that the effect of population trapping does not necessarily require decoupling of the antisymmetric superposition from the dissipative interactions. We also find that the vacuum-induced coherent coupling between the systems could be easily observed in Lambda-type atoms. Our analysis of the population trapping in two nonidentical atoms shows that the atoms can be driven into a maximally entangled state which is completely decoupled from the dissipative interaction.

Measuring the decoherence rate in a semiconductor charge qubit

We describe a method by which the decoherence time of a solid-state qubit may be measured. The qubit is coded in the orbital degree of freedom of a single electron bound to a pair of donor impurities in a semiconductor host. The qubit is manipulated by adiabatically varying an external electric field. We show that by measuring the total probability of a successful qubit rotation as a function of the control field parameters, the decoherence rate may be determined. We estimate various system parameters, including the decoherence rates due to electromagnetic fluctuations and acoustic phonons. We find that, for reasonable physical parameters, the experiment is possible with existing technology. In particular, the use of adiabatic control fields implies that the experiment can be performed with control electronics with a time resolution of tens of nanoseconds.

Controlling the decoherence of a ''meter'' via stroboscopic feedback

We propose a simple modification of the experimental scheme employed by Brune rt ni. [Phys. Rev. Lett. 79, 4887 (1996)] for the generation and detection of a Schrodinger cat state, in which the decoherence of the cat state can be significantly slowed down using an appropriate feedback.