arXiv subjects
Publications and source records attributed to Daniel F. V. James.
We analyze nonlinear coupling between individual vibrational quanta for trapped ions. The nonlinear Coulomb interaction causes a Kerr-type Hamiltonian, for which we derive an analytical expression for the coupling constant. In contrast to a previously published formula [1], our result is in close agreement with experimental data.
We study the dynamics of entanglement in continuous variable quantum systems (CVQS). Specifically, we study the phenomena of Entanglement Sudden Death (ESD) in general two-mode-N-photon states undergoing pure dephasing. We show that for these states, ESD never occurs. These states are generalizations of the so-called High NOON states, shown to decrease the Rayleigh limit of lambda to lambda/N, which promises great improvement in resolution of interference patterns if states with large N are physically realized. However, we show that in dephasing NOON states, the time to reach V_crit, critical visibility, scales inversely with N^2. On the practical level, this shows that as N increases, the visibility degrades much faster, which is likely to be a considerable drawback for any practical application of these states.
In this paper, we examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum state tomography. We find that, in some important circumstances, an elaborate and time-consuming numerical optimization to obtain 'the best' density matrix corresponding to a given data set is not necessary, and that cruder, faster numerical techniques may well be 'good enough'.
In this paper we consider the decay of quantum entanglement, quantified by the concurrence, of a pair of two-level systems each of which is interacting with a reservoir at finite temperature T. For a broad class of initially entangled states, we demonstrate that the system always becomes disentangled in a finite time i.e."entanglement sudden death" (ESD) occurs. This class includes all states which previously had been found to have long-lived entanglement in zero temperature reservoirs. Our general result is illustrated by an example.
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To illustrate the technique we give examples involving Raman processes, Bloch-Siegert shifts and Quantum Logic Gates.
We examine in detail the theory of the intrinsic non-linearities in the dynamics of trapped ions due to the Coulomb interaction. In particular the possibility of mode-mode coupling, which can be a source of decoherence in trapped ion quantum computation, or, alternatively, can be exploited for parametric down-conversion of phonons, is discussed and conditions under which such coupling is possible are derived.
We consider the feasibility of performing quantum logic operations based on stimulated Raman transitions in trapped Calcium ions. This technique avoids many of the technical difficulties involved with laser stabilisation, and only three laser wavelengths are required, none of which need have particularly stringent requirements on their bandwidths. The possible problems with experimental realisations are discussed in detail.
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (``qubits''). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices which are always non-negative definite). In addition a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.
Classical and quantum dynamics of a harmonic oscillator in a monochromatic wave is studied in the exact resonance and near resonance cases. This model describes, in particular, a dynamics of a cold ion trapped in a linear ion trap and interacting with two lasers fields with close frequencies. Analytically and numerically a stability of the ``classical ground state'' (CGS) -- the vicinity of the point ($x=0, p=0$) -- is analyzed. In the quantum case, the method for studying a stability of the quantum ground state (QGS) is suggested, based on the quasienergy representation. The dynamics depends on four parameters: the detuning from the resonance, $δ=\ell-Ω/ω$, where $Ω$ and $ω$ are, respectively, the wave and the oscillator's frequencies; the positive integer (resonance) number, $\ell$; the dimensionless Planck constant, $h$, and the dimensionless wave amplitude, $ε$. For $δ=0$, the CGS and the QGS are unstable for resonance numbers $\ell=1, 2$. For small $ε$, the QGS becomes more stable with increasing $δ$ and decreasing $h$. When $ε$ increases, the influence of chaos on the stability of the QGS is analyzed for different parameters of the model, $\ell$, $δ$ and $h$.
Using a spontaneous-downconversion photon source, we produce true non-maximally entangled states, i.e., without the need for post-selection. The degree and phase of entanglement are readily tunable, and are characterized both by a standard analysis using coincidence minima, and by quantum state tomography of the two-photon state. Using the latter, we experimentally reconstruct the reduced density matrix for the polarization. Finally, we use these states to measure the Hardy fraction, obtaining a result that is $122 σ$ from any local-realistic result.
We present a novel method of performing quantum logic gates in trapped ion quantum computers which does not require the ions to be cooled down to their vibrational center of mass (CM) mode ground state. Our scheme employs adiabatic passages and the conditional phase shift first investigated by D'Helon and Milburn (C.~D'Helon and G.J.~Milburn, Phys. Rev. A {\bf 54}, 5141 (1996)).
We consider a simple model, based on currently accepted models for active galactic nuclei, for a quasi-stellar object (QSO or ``quasar'') and examine the influence that correlation- induced spectral changes (``The Wolf Effect'') may have upon the redshifts of the optical emission lines.
Using a displacement operator formalism, I analyse the depopulation of the vibrational ground state of trapped ions. Two heating times, one characterizing short time behaviour, the other long time behaviour are found. The short time behaviour is analyzed both for single and multiple ions, and a formula for the relative heating rates of different modes is derived. The possibility of correction of heating via the quantum Zeno effect, and the exploitation of the suppression of heating of higher modes to reduce errors in quantum computation is considered.
The theory of interactions between lasers and cold trapped ions as it pertains to the design of Cirac-Zoller quantum computers is discussed. The mean positions of the trapped ions, the eigenvalues and eigenmodes of the ions' oscillations, the magnitude of the Rabi frequencies for both allowed and forbidden internal transitions of the ions and the validity criterion for the required Hamiltonian are calculated. Energy level data for a variety of ion species is also presented.
Using simple physical arguments we investigate the capabilities of a quantum computer based on cold trapped ions. From the limitations imposed on such a device by spontaneous decay, laser phase coherence, ion heating and other sources of error, we derive a bound between the number of laser interactions and the number of ions that may be used. The largest number which may be factored using a variety of species of ion is determined.