Decoherence time / rate

It is important to point out that even at 77 = 0 the observed value V = 0.942 0.006 is far from its ideal value of V = 0. One important source of error is the finite retrieval efficiency, which is limited by two factors. Due to the atomic memory decoherence rate 7C, the finite retrieval time Tr always results in a finite loss probability p 7c Tr. For the correlation measurements we use a relatively weak retrieve laser ( 2 mW) to reduce the number of background photons and to avoid APD dead-time effects. The resulting anti-Stokes pulse width is on the order of the measured decoherence time, so the atomic excitation decays before it is fully retrieved. Moreover, even as 7C —> 0 the retrieval efficiency is limited by the finite optical depth q of the ensemble, which yields an error scaling as p 1/ y/rj. The measured maximum retrieval efficiency at 77 = 0 corresponds to about 0.3. In addition to finite retrieval efficiency, many other factors reduce correlations, including losses in the detection system, background photons, APD afterpulsing effects, and imperfect spatial mode-matching. 

The characteristic decoherence time for this copper complex has been found to be slightly below 10 fs for both complexes, whatever the direction of the reaction (S—>T or T—>S) Table 1. The computed hopping probabilities entering the transmission coefficient of the rate constant show an interesting feature the introduction of a sulfur atom within the copper coordination sphere induces an increase of the hopping probability by a factor of more than 3. These effects are related to the... 

The ASE process occurs in a gain medium whenever the optical confinement is superior, or the decoherence time is short (Section 22.2). The confinement can be described by the radiation leakage rate k, whereas the cooperation among chromophores may be quantified by the Arrechi-Courtens time [112] Tc, which is inversely proportional to the chromophore density in the medium. The value of (kTc) accounts for the relative number of photons emitted by the ASE process [96]. This happens in both polymer solutions (in a cuvette), or in neat polymer films of thickness 100 nm deposited on glass substrates due to optical confinement formed by the film waveguiding properties. 

The first part of the chapter focuses on the derivation of a mixed quantum-classical theory for rationalizing chemical reactions involving two electronic states. The central piece of this mixed quantum-classical rate constant is the appearance of a characteristic decoherence time. The second part of the chapter deals with numerical approaches at the atomic level that can be carried out to decipher the molecular mechanisms governing decoherence in real systems of biological interest. 

Lockwood and colleagues performed an analysis of decoherence in a ruthenium-modified blue copper protein similar to amicyanin. They found a short characteristic decoherence time of 2.4 fs, which they attributed on one hand to the diverging motion of the protein nuclei and on the other hand to the solvent molecules. Their conclusion was that both solvent and protein dynamics can affect both the rate and mechanism of electron transfer which is different to our conclusions on solvated TTQ where the solvent does not seem to play any role in decoherence. More precisely, solvent molecules start to play a role once decoherence has already occurred due to the intramolecular motions within the TTQ. Lockwood et al. used a classical force field for all the atoms, including those of the copper and ruthenium complexes, and a rigid SPC water model. In addition they did not carry out large ensembles of diverging... 

The results presented Irom vibrational relaxation calculations show that the method is numerically very feasible and that the short time approximatiorrs are welljustified as long as the energy difference between the initial and final quantum states is not too small. It is also found that the crossover from the early time quantiun regime to the rate constant regime can be due to either phase decoherence or due to the loss of correlation in the coupling between the states, or to a combination of these factors. The methodology described in Section n.C has been formulated to account for both of these mechanisms. 

We have applied the above approach to a harmonic oscillator coupled to a spin by means of a photon number - nondemolition Hamiltonian. The spin is being measured periodically, whereas the measurement outcome is ignored. For a sufficiently high measurement frequency, the state of the harmonic oscillator evolves in a unitary manner which can be influenced by a choice of the meter basis. In practice however, the time interval At between two subsequent measurements always remains finite and, therefore, the system evolution is subject to decoherence. As an example of application, we have simulated the evolution of an initially coherent state of the harmonic oscillator into a Schrodinger cat-like superposition state. The state departs from the superposition as time increases. The simulations confirm that the decoherence rate increases dramatically with the amplitude of the initial coherent state, thus destroying very rapidly all macroscopic superposition states. 

To sum up, our treatment has elucidated the short-time dynamics of low-temperature MQT through time-modulated barriers. Current-bias modulation has been shown to imitate either frequent measurements or correlated perturbations of a decaying state, between successive impulses (shocks) [Fan-dau 1977 Ivlev 2002], Such modulation has been demonstrated to either enhance or suppress the MQT rate (causing the AZE or QZE, respectively). Remarkably, quantum gates based on JJ qubits [Averin 2000] or their atomic-condensate counterparts [Smerzi 1997 Anderson 1998 (a)] may benefit from the ability to suppress the decoherence due to MQT to the continuum. 

To create a quantum computation system based on a qubit ensemble and to decrease the required magnetic field and its gradient the modification of the cluster structure was proposed [1,2]. It consists in utilization of nuclear spin chains on the steps of the silicon surface which serve as the qubit ensemble. Resonance frequencies of a magnetic isotope nucleus 29Si are divided between neighboring chains. In this case the efficiency of quantum computation is determined by the decoherence rate for a quantum state. The decoherence rate depends on the number of nucleus in a qubit and on the time of transverse relaxation of nuclear spin polarization. The aim of the present work is calculation of the decoherence rate of the quantum state of the qubit ensemble built on the basis of these nuclei. 

Decoherence rate Vdcc is determined as an inversion of decay time of the signal (1/e) depending on the coherence order M. Possibility of qubit measuring also depends on M. When the coherence order is increasing, the signal level and Vdec are growing. 

The interference terms (and therefore also the hydrogen anomalies discussed above) appear only as long as coherence is maintained in the neutron-proton interaction. Here, it should be noted that Zsc is an average scattering time in a set of events. The probability for each individual event (which happens within the nuclear time 10 s) goes as P(f) = P(f = 0)e " with Zsc determined by Eq. (22.1). However, with an external decoherence rate I/Tcoh, the probability for a preserved coherence changes to... 

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