Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach

We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD's) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system state depends on the actual current through the PC device, we use the so-called quantum trajectory method to derive the zero-temperature conditional master equation. We first treat the electron tunneling through the PC barrier as a classical stochastic point process (a quantum-jump model). Then we show explicitly that our results can be extended to the quantum-diffusive limit when the average electron tunneling rate is very large compared to the extra change of the tunneling rate due to the presence of the electron in the dot closer to the PC. We find that in both quantum-jump and quantum-diffusive cases, the conditional dynamics of the CQD system can be described by the stochastic Schrodinger equations for its conditioned state vector if and only if the information carried away from the CQD system by the PC reservoirs can be recovered by the perfect detection of the measurements.

Quantum slow motion

We investigate the center-of-mass motion of cold atoms in a standing amplitude modulated laser field. We use a simple model to explain the momentum distribution of the atoms after any distinct number of modulation cycles. The atoms starting near a classical phase-space resonance move slower than we would expect classically. We explain this by showing that for a wave packet on the classical resonances we can replace the complicated dynamics in the quantum Liouville equation in phase space by its classical dynamics with a modified potential.

Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement

We present the conditional quantum dynamics of an electron tunneling between two quantum dots subject to a measurement using a low transparency point contact or tunnel junction. The double dot system forms a single qubit and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dot. We illustrate the difference between conditional and unconditional dynamics of the qubit. The conditional dynamics is discussed in two regimes depending on the rate of tunneling through the point contact: quantum jumps, in which individual electron tunneling current events can be distinguished, and a diffusive dynamics in which individual events are ignored, and the time-averaged current is considered as a continuous diffusive variable. We include the effect of inefficient measurement and the influence of the relative phase between the two tunneling amplitudes of the double dot/point contact system.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

The effects of time delays in adaptive phase measurements

It is not possible to make measurements of the phase of an optical mode using linear optics without introducing an extra phase uncertainty. This extra phase variance is quite large for heterodyne measurements, however it is possible to reduce it to the theoretical limit of log (n) over bar (4 (n) over bar (2)) using adaptive measurements. These measurements are quite sensitive to experimental inaccuracies, especially time delays and inefficient detectors. Here it is shown that the minimum introduced phase variance when there is a time delay of tau is tau/(8 (n) over bar). This result is verified numerically, showing that the phase variance introduced approaches this limit for most of the adaptive schemes using the best final phase estimate. The main exception is the adaptive mark II scheme with simplified feedback, which is extremely sensitive to time delays. The extra phase variance due to time delays is considered for the mark I case with simplified feedback, verifying the tau /2 result obtained by Wiseman and Killip both by a more rigorous analytic technique and numerically.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

Critical quantum fluctuations in the degenerate parametric oscillator

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

Polarization squeezing and continuous-variable polarization entanglement

A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.

Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Coherent superposition states as quantum rulers

We explore the sensitivity of an interferometer based on a quantum circuit for coherent states. We show that its sensitivity is at the Heisenberg limit. Moreover, we show that this arrangement can measure very small length intervals.

Quantum Parrondo's games

Parrondo's paradox arises when two losing games are combined to produce a winning one. A history-dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general SU(2) operators to transform the game into the quantum domain. In the initial state, a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case. (C) 2002 Elsevier Science B.V. All rights reserved.

The impact of CdSe/ZnS Quantum Dots in cells of Medicago sativa in suspension culture

Abstract Background: Nanotechnology has the potential to provide agriculture with new tools that may be used in the rapid detection and molecular treatment of diseases and enhancement of plant ability to absorb nutrients, among others. Data on nanoparticle toxicity in plants is largely heterogeneous with a diversity of physicochemical parameters reported, which difficult generalizations. Here a cell biology approach was used to evaluate the impact of Quantum Dots (QDs) nanocrystals on plant cells, including their effect on cell growth, cell viability, oxidative stress and ROS accumulation, besides their cytomobility. Results: A plant cell suspension culture of Medicago sativa was settled for the assessment of the impact of the addition of mercaptopropanoic acid coated CdSe/ZnS QDs. Cell growth was significantly reduced when 100 mM of mercaptopropanoic acid -QDs was added during the exponential growth phase, with less than 50% of the cells viable 72 hours after mercaptopropanoic acid -QDs addition. They were up taken by Medicago sativa cells and accumulated in the cytoplasm and nucleus as revealed by optical thin confocal imaging. As part of the cellular response to internalization, Medicago sativa cells were found to increase the production of Reactive Oxygen Species (ROS) in a dose and time dependent manner. Using the fluorescent dye H2DCFDA it was observable that mercaptopropanoic acid-QDs concentrations between 5-180 nM led to a progressive and linear increase of ROS accumulation. Conclusions: Our results showed that the extent of mercaptopropanoic acid coated CdSe/ZnS QDs cytotoxicity in plant cells is dependent upon a number of factors including QDs properties, dose and the environmental conditions of administration and that, for Medicago sativa cells, a safe range of 1-5 nM should not be exceeded for biological applications.

Studying nanotoxic effects of CdTe quantum dots in Trypanosoma cruzi

Semiconductor nanoparticles, such as quantum dots (QDs), were used to carry out experiments in vivo and ex vivo with Trypanosoma cruzi. However, questions have been raised regarding the nanotoxicity of QDs in living cells, microorganisms, tissues and whole animals. The objective of this paper was to conduct a QD nanotoxicity study on living T. cruzi protozoa using analytical methods. This was accomplished using in vitro experiments to test the interference of the QDs on parasite development, morphology and viability. Our results show that after 72 h, a 200 μM cadmium telluride (CdTe) QD solution induced important morphological alterations in T. cruzi, such as DNA damage, plasma membrane blebbing and mitochondrial swelling. Flow cytometry assays showed no damage to the plasma membrane when incubated with 200 μM CdTe QDs for up to 72 h (propidium iodide cells), giving no evidence of classical necrosis. Parasites incubated with 2 μM CdTe QDs still proliferated after seven days. In summary, a low concentration of CdTe QDs (2 μM) is optimal for bioimaging, whereas a high concentration (200 μM CdTe) could be toxic to cells. Taken together, our data indicate that 2 μM QD can be used for the successful long-term study of the parasite-vector interaction in real time.

Microscopic and macroscopic polarization within a combined quantum mechanics and molecular mechanics model

A polarizable quantum mechanics and molecular mechanics model has been extended to account for the difference between the macroscopic electric field and the actual electric field felt by the solute molecule. This enables the calculation of effective microscopic properties which can be related to macroscopic susceptibilities directly comparable with experimental results. By seperating the discrete local field into two distinct contribution we define two different microscopic properties, the so-called solute and effective properties. The solute properties account for the pure solvent effects, i.e., effects even when the macroscopic electric field is zero, and the effective properties account for both the pure solvent effects and the effect from the induced dipoles in the solvent due to the macroscopic electric field. We present results for the linear and nonlinear polarizabilities of water and acetonitrile both in the gas phase and in the liquid phase. For all the properties we find that the pure solvent effect increases the properties whereas the induced electric field decreases the properties. Furthermore, we present results for the refractive index, third-harmonic generation (THG), and electric field induced second-harmonic generation (EFISH) for liquid water and acetonitrile. We find in general good agreement between the calculated and experimental results for the refractive index and the THG susceptibility. For the EFISH susceptibility, however, the difference between experiment and theory is larger since the orientational effect arising from the static electric field is not accurately described

Vertically coupled quantum dots in the local spin-density functional theory

We have investigated the structure of double quantum dots vertically coupled at zero magnetic field within local-spin-density functional theory. The dots are identical and have a finite width, and the whole system is axially symmetric. We first discuss the effect of thickness on the addition spectrum of one single dot. Next we describe the structure of coupled dots as a function of the interdot distance for different electron numbers. Addition spectra, Hund's rule, and molecular-type configurations are discussed. It is shown that self-interaction corrections to the density-functional results do not play a very important role in the calculated addition spectra