Session P33: Quantum Mechanical Properties

Teleportation of electronic many-qubit states via single photons

We propose a teleportation scheme that relies only on single- photon measurements and Faraday rotation, for teleportation of many-qubit entangled states stored in the electron spins of a quantum dot system. The interaction between a photon and the two electron spins, via Faraday rotation in microcavities, establishes Greenberger-Horne-Zeilinger entanglement in the spin-photon-spin system. The appropriate single-qubit measurements, and the communication of two classical bits, produce teleportation. This scheme provides the essential link between spintronic and photonic quantum information devices by permitting quantum information to be exchanged between them.   

Coherence-decoherence crossover with subohmic bath

We study the spin-boson model with a subohmic bosonic bath using variational method. The coherence-decoherence crossover for a finite two-level splitting is analyzed. The results for the crossover as a function of temperature and strength of the bath will be discussed.   

A quantum measurement of the double barrier junction (DBJ) qubit

A quantum measurement on a double barrier junction (DBJ) qubit performed by a coupled by an SIS junction is studied. The DBJ qubit state $\left| s\right\rangle$ is monitored by entangling of it with the SIS ``meter'' state $\left| m\right\rangle$. The the coupling strength $J$ between the ABS qubit and the meter is controlled by a Josephson flux transistor. The efficiency of the measurement versus the coupling strength between DBJ and SIS is computed. It is found that the information gained in the quantum measurement depends on $J$ and on the ratio $\mu =\varepsilon_m /\varepsilon_q$ (where $\varepsilon_q$ and $\varepsilon_m$ are the qubit and the meter level splitting correspondingly. Using a linear circuit approach we also compute the spectral density $J_{eff}^s (\omega )$ of the qubit noise induced during the measurement. An evaluation of noise and decoherence made shows that they depend on the characteristic times of the equivalent circuit of the qubit system, and thus may be optimized to improve the overal qubit performance.   

Quantum measurement of a Cooper-Pair Box using a nanomechanical resonator

It has been shown by Irish and Schwab that the resonant frequency of a nanomechanical resonator depends on the quantum state of the Cooper-Pair box (CPB) coupled to it. In addition, the energy splitting of the CPB is shifted as a result of the interaction with the resonator. We explore the possibility of using the nanomechanical resonator to detect the state of a CPB at degeneracy. We also discuss the possibility of making quantum nondemolition measurements of Fock states of the nanomechanical resonator by probing the energy levels of the CPB. We will describe our experimental progress where we are currently working with a 10 MHz resonator which is capacitively coupled to the CPB. The resonator is read out using our newly developed impedance matched, capacitive technique.   

Noise and Back-action in Nanomechanical Resonators

We have recently demonstrated that a superconducting Single Electron Transistors (SSET) capacitively coupled to a nanomechanical resonator, can be used as a nearly-quantum limited position detector. The ultimate sensitivity of this scheme is limited both by forward-coupled charge fluctuations on the SET island and back-acting electrostatic potential fluctuations which drive the resonator. In this talk, we will present our recent measurements of SET back-action on nano-resonators. In particular, we will discuss the back-coupled power, damping, and frequency of the resonance as a function of the coupling between the SET and the resonator and compare these results to theoretical predictions.   

Non-Markovian qubit dynamics in a thermal field bath: Relaxation, decoherence and entanglement

We have studied the non-Markovian dynamics of a qubit interacting with an electromagnetic field bath initially at finite temperature in the Jaynes-Cummings model. Unlike studies in which the bath is assumed to be fixed, we have included the dynamics of the bath, thus allowing for the coherent evolution of the combined qubit-bath system. In this way we can see the development of quantum correlations and entanglement between the system and its environment. The non-Markovian effects are illustrated in various quantities including the decoherence, relaxation, fidelity and von~Neumann entropy, which are compared to the Markovian results.   

Quantum Adiabatic Evolution Algorithm via combinatorial landscapes

We analyze the performance of the Quantum Adiabatic Evolution algorithm (QAEA) on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $g=M/N$. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (versus only energy) is used, and are able to show the existence of a dynamic threshold $g=g_d$, beyond which QAEA should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz. We have been able to map the ensemble of random graphs onto another ensemble with fluctuations significantly reduced. This enabled us to obtain tight upper bounds on satisfiability transition and to recompute the dynamical transition using the extended set of landscapes.   

Effects of finite bandwidth and delay on Bayesian quantum feedback of a qubit

We analyze the effect of various imperfections on the performance of the Bayesian quantum feedback loop designed to maintain quantum coherent oscillations in a solid-state ``charge'' qubit for an arbitrary long time. For the feedback operation the qubit state is continuously monitored using the information provided by the noisy output of a weakly coupled detector (quantum point contact or single-electron transistor); this information is taken into account using the quantum Bayesian equations. Finite signal bandwidth reduces the monitoring accuracy and affects performance of the feedback; we study this effect by Monte Carlo simulation of the quantum measurement process. We also analyze the reduction of feedback fidelity due to additional time delay in the control loop. The simulations also take into account finite quantum efficiency of the detector and possible energy asymmetry of the qubit.   

Experimental Evidence for Violation of Bohr's Principle of Complementarity

We have implemented a novel double-slit which-way experiment which raises interesting questions of interpretation. Coherent laser light passes through a dual pinhole, and the resulting interference pattern is passed through a converging lens which produces well-resolved images of the two pinholes, providing full which-way information. A series of thin wires are then placed at the minima of the interference pattern upstream of the lens. No reduction in the total flux or resolution of the images is found, providing evidence for coexistence of perfect interference and which-way information in the same experiment, contrary to the common readings of Bohr's principle of complementarity. Implications of the experiment for the measurement theory are also briefly discussed.   

Interference and Trajectories

A trajectory representation of interference is presented. The trajectory representation manifests destructive interference and reinforcement as a dwell-time phenomenon of the trajectory. Evoking a probability density is unnecessary.   

Inference of Schr\"odinger's Equation from Classical Wave Mechanics[1]

A localized oscillatory point charge $q$ generates in a one-dimensional box electromagnetic waves which may be generally described by monochromatic plane waves $\{\varphi_i=C_K e^{i(KX- \Omega T+ \alpha_i)}\}$ of angular frequency $\Omega$, wavevector $K=\Omega/c$, velocity (of light) $c$, and initial phases $\{\alpha_i\}$. $q$ and $\{\varphi_i\}$ as a whole is here taken as a particle, which total energy ${\sf E}$ and mass $M$ are given by the basic equations ${\sf E}=\hbar \Omega=M c^2 $, $2\pi\hbar$ being Planck constant. (For example, $q=-e$ and $M=511$ keV give an electron.) $\{\varphi_i\}$ as incident and reflected and those from the charge as reflected in the box superimpose into a total wave $\psi=\sum \varphi_i$ that, as with $\varphi_i$, obeys the classical wave equation (CWE): $c^2 \frac{d^2\psi}{d X^2}= \frac{d^2\psi}{d T^2}$. If now the particle is traveling at velocity $v$, in a potential field $V=0 $ here (see Ref. 2004b for $V\ne 0$), then $\{\varphi_i'\}$ are Doppler effected and form a total wave $\psi'={\mit\Phi} {\mit\Psi}$, with ${\mit\Psi}= C \sin(K_d X)e^{i \Omega_d T}$ being the envelope about a beat wave and identifiable as de Broglie wave of angular frequency $\Omega_d= \Omega (v/c)^2$, and ${\mit \Phi}$ an undisplaced monochromatic wave. Using $\psi'$ in CWE gives upon decomposition a separate equation describing the particle dynamics, $-\frac{\hbar^2}{2M} \frac{\partial^2 {\mit\Psi}(X,T)}{\partial X^2}=i\hbar\frac {\partial {\mit\Psi}(X,T)}{\partial T}$, which is equivalent to Schr\"odinger's equation. \\[0cm] [1] J. X. Zheng-Johansson and P-I. Johansson, arXiv:Physics/0411134 (2004a); "Unification of Classical, Quantum and Relativistic Mechanics and the Four Forces" (in printing, 2004b).