Coherence time

For the stretching oscillations of the CFI cliromophore in CFIF3 100 fs. Clearly, typical coherence time... 

The time period A/ia which the light wave undergoes random changes is called the coherence time. It is related to the Hnewidth Av of the laser by the equation... 

For exposures much longer than the atmospheric coherence time (T tq), the image is formed by the average of many short exposure images,... 

Adaptive optics requires a reference source to measure the phase error distribution over the whole telescope pupil, in order to properly control DMs. The sampling of phase measurements depends on the coherence length tq of the wavefront and of its coherence time tq. Both vary with the wavelength A as A / (see Ch. 1). Of course the residual error in the correction of the incoming wavefront depends on the signal to noise ratio of the phase measurements, and in particular of the photon noise, i.e. of the flux from the reference. This residual error in the phase results in the Strehl ratio following S = exp —a ). 

Let us first consider the case where the laser beam is emitted through the telescope. The outgoing beam undergoes a tilt deflection through the turbulent atmosphere as does the backscattered light. The round trip time to the mesosphere is 0.6 ms at zenith. It is much shorter than the tilt coherence time ... 

At an 8m telescope in a good site, ro 0.15m and a wind velocity of V 30m/s, To,tilt 0.12 s at A = 0.5/xm to 1.2 s at A = 5/rm. It scales as A. To,tilt is 10 times larger than the wavefront coherence time. Thus both deflections to and from the mesosphere approximately cancel each other and the LGS apparent location is fixed with respect to the optical axis. The principle of inverse return of light applies one does not know the LGS location in the sky, and the tilt cannot be measured. 

In the hrst case, the degree of self coherence depends on the spectral characteristics of the source. The coherence time Tc represents the time scale over which a held remains correlated this hme is inversely proportional to the spectral bandwidth Au) of the detected light. A more quantitative dehnition of quasi-monochromatic conditions is based on the coherence time all relevant delays within the interferometer should be much shorter than the coherence length CTc. A practical way to measure temporal coherence is to use a Michel-son interferometer. As we shall see, in the second case the spatial coherence depends on the apparent extent of a source. 

It is interesting to note that to actually implement a useful algorithm it is necessary to implement a certain number of quantum operations within the coherence time. Recently, we reported that it was possible to increase the number of coherent rotations by a factor of 10 by matching the Rabi frequency with the frequency of the proton in the polyoxometalate SIM GdW30. Under these conditions, it was possible to perform at least 80 such operations (Figure 2.14) [75]. 

As an alternative to QDs, silicon can be doped with single atom impurities, in particular phosphorus, which acts as an electron donor. Donors can be implanted individually with a precision of about 10 nm. Either the 31P nuclear spin or the unpaired electron can be used as qubits [63, 64]. An advantage of silicon is its widespread use in current electronics, meaning that QC might profit from methods and technologies already developed for their classical cousins . Also, spins in silicon can attain extremely high coherence times experiments on 28 Si-enriched silicon show spin coherence times T2 exceeding 10 s [65]. The read-out and coherent manipulation of individual spin qubits in silicon have been recently achieved [66]. 

Lanthanide ions offer several salient properties that make them especially attractive as qubit candidates (i) their magnetic states provide proper definitions of the qubit basis (ii) they show reasonably long coherence times (iii) important qubit parameters, such as the energy gap AE and the Rabi frequency 2R, can be chemically tuned by the design of the lanthanide co-ordination shell and (iv) the same molecular structure can be realized with many different lanthanide ions (e.g. with or without nuclear spin), thus providing further versatility for the design of spin qubits or hybrid spin registers. 

The SH intensity is proportional to P 2. Experimentally, the oscillatory part of the total SH is so small that one can ignore its second-order term. If coherent surface phonons are created by ISRS, the whole process including excitation and detection is the coherent time-domain analogue of stimulated hyper Raman scattering (y(4) process) [14]. The cross section of the SHG process is then proportional to the product of a Raman tensor in the pump transition and a hyper-Raman tensor dx k/dQn in the probe transition. 

A further important property of a MQC description is the ability to correctly describe the time evolution of the electronic coefficients. A proper description of the electronic phase coherence is expected to be particularly important in the case of multiple curve-crossings that are frequently encountered in bound-state relaxation dynamics [163]. Within the limits of the classical-path approximation, the MPT method naturally accounts for the coherent time evolution of the electronic coefficients (see Fig. 5). This conclusion is also supported by the numerical results for the transient oscillations of the electronic population, which were reproduced quite well by the MFT method. Similarly, it has been shown that the MFT method in general does a good job in reproducing coherent nuclear motion on coupled potential-energy surfaces. 

It is crucial to attain high coherence time T. In the beam experiments that time is just the time of flight through the region with the electric held. For a gas-dynamic molecular source the typical time of flight is 1 — 10 ms. On the other hand, for the PbO experiment in vapor cell T is close to the lifetime of the excited (metastable) state a(l), T 0.1 Ills. So, the beam experiments have advantage in the coherence time. 

Consider one resolution cell xm of the spectrum. The number of df, zm, is defined as the number of independent volumes that exist over the volume swept out by photons leaving the entrance slit during one exposure time t (see Fig. 3). An independent volume is the three-dimensional space over which a photon is coherent. Hence, if it has a coherence length c Arm, with c the speed of light and Arm the coherence time, and if it has a coherence area cTm, the coherence volume is simply their product, or c Arm om. On the other hand, the total volume swept out by a wave front of photons all leaving the aperture of area A during exposure time t is ctA. Hence the number of coherence volumes is... 

The coherence time Axm relates to abscissa xm and resolution interval Ax as follows. By the Heisenberg uncertainty principle, Axm goes inversely with spectral purity, or... 

Recently, we have shown that whenever qubits collectively couple to common bath modes (e.g., in ion traps [119,120] or cavities [121-123]) local modulations of individual qubits can eliminate cross-decoherence. Our major result is that the modulation must be faster than the correlation time of the bath, but can be much slower than the (unmodulated) multipartite coherence time and still be effective. 

Fig. 2. Photon echo spectra vs. population time (a, d) and coherence time (b, c, e, 1) at fixed other delay time for pump or probe pulse wavelength at the maximum (575 nm) and on the blue side (560 nm) of the absorption maximum. The inset shows the contour plot of corresponding figure...

The spectra measured at each of a range of different coherence times ti2 and population times t23 can be different because the wavelengths of k2 and k3 are not the same. When the pump wavelength is shorter than the probe, we observe ... 

By contrast, when the pump wavelength is longer than the probe, enhancement of the echo signal occurs on the blue side when scanning either the coherence time (fig. 2e, 2f and fig. 3e, 3f) or the population time (fig. 2d and fig. 3d). These results are interpreted as reflecting the dynamics of vibration in the electronic ground state (Feynman diagrams (c),(d)). 

Scanning of the population time in these experiments yields detailed information about the vibrational relaxation and scanning of the coherence time allows a study of the splitting of the vibrational levels. 

---