Decoherence time

Figure 7.9 (a) Echo-detected X-band EPR spectrum of a powder sample of Gd001 Y099W30 at T = 6 K. (b) Decoherence times 7, (solid symbols) and T2 (open symbols) measured at fi0H = 0.347 T, as a function of the atomic concentration of Gd ions. 

The finite decoherence time is due to some inelastic scattering mechanism inside the system, but typically this time is shorter than the energy relaxation time re, and the distribution function of electrons inside the system can be nonequilibrium (if the finite voltage is applied), this transport regime is well known in semiconductor superlattices and quantum-cascade structures. 

Research on modeling of endohedral fullerenes within single-walled carbon nanotubes (SWNTs) has received increased attention towards the understanding of their electronic and structural properties [304-307]. However, very recently particular emphasis was given to the endohedral fullerenes N C60 [308-313] and P C60 [314] due to the electron spin on the nitrogen or phosphorus site, respectively. Having an extremely long decoherence time the unpaired electron spin could be used as a qubit within a quantum computer. 

In the specific case where, 4) and B) are two coherent states of the same macroscopic oscillator, located at a distance Ax apart from one another, it is shown [108] that the picture based on the prescription of the Hamiltonian of Eq. (258) can be maintained provided that we set the condition g2(c2) = (Ax)2 , where is a parameter proportional to the product of temperature and friction. The details of this calculation are not important for this review. Therefore let us limit ourselves to observing that this procedure yields for the decoherence time the expression... 

The important fact is that the decoherence time may become so small as to ensure that there is no room for the superposition condition A) + B) in classical physics, if A) and B) correspond to two distinct positions, macroscopically distant from one another. 

In practice, decay of the spin coherence during the delay time t,i and finite optical depth flatten and broaden the anti-Stokes pulse, reducing the total number of anti-Stokes photons which can be retrieved within the coherence time of the atomic memory. For weak retrieve laser intensities, the total photon number per pulse increases with increasing laser power because the time required to read out the spin wave is longer than the characteristic decoherence time of our atomic memory ( 3gs, see Fig. 3 b). After accounting for dead-time effects, we find that once the retrieve laser power increases to 25 mW, all of the spin wave is retrieved in a time shorter than the decoherence time, resulting in a constant anti-Stokes number versus retrieve power. 

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 above results are applied to a harmonic oscillator coupled to a two-level system, that serves as the repeatedly measured ancilla. Relatively sparse measurements are shown to destroy the coherence of the oscillator whereas, in the Zeno-limit, the coherence is preserved for all times. This is demonstrated by a periodic generation of a Schrodinger cat-like state. The decoherence process is highly nonlinear in the initial state amplitude and the decoherence time decreases rapidly for increasing amplitude. 

Diffraction experiments are carried out by thermal neutrons and with observation times of 10 13 s or more. These experiments indicate that H - H entanglement survives over an unusually long time in this particular compound. The reason for the long decoherence time was discussed in Ref. [Fillaux 1998] as a result of restricted coupling of the H - H dimers to the KII( () >, environment caused by specific fermion / boson superselection rules. 

The pump-probe pulses are obtained by splitting a femtosecond pulse into two equal pulses for one-color experiments, or by frequency converting a part of the output to the ultraviolet region for bichromatic measurements. The relative time delay of the two pulses is adjusted by a computer-controlled stepping motor. Petek and coworkers have developed interferometric time-resolved 2PPE spectroscopy in which the delay time of the pulses is controlled by a piezo stage with a resolution of 50 attoseconds [14]. This set-up made it possible to probe decoherence times of electronic excitations at solid surfaces. 

Measurements of the quantum coherence are usually performed in dilute systems to prevent decoherence due to fluctuating intermolecular magnetic-dipolar electron-electron interactions. In SMMs these fluctuations can also be frozen out at low temperatures, below the blocking temperature of the magnetization. A singlecrystal study on Feg made use of this fact and, indeed, phase memory times of up to 712 ns were observed at 1.27 K [153]. Raising the temperamre to 1.93 K results in a drastic reduction of Tm to 93 ns. Simulations showed that electron spin-electron spin interactions can account quantitatively for this behavior. A second decoherence process was identified from these simulations, with a decoherence time of about 1 ps, which was attributed to hyperfine-induced decoherence. 

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... 

Fig. 10 Three-step cranpntational protocol employed to estimate decoherence times with deMon2k. The orange and cyan Gaussian functions along the left-hand side set of diverging trajectory represent one unclear wave packet on the singlet and triplet PES...

Table 1 Decoherence time and average hopping probabiUties for the N2N- and N2S-based [Cu02] adducts following the computational protocol described in [142] that is based on DPT MD simulations...

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