Coherent states switching

Such a tunnel switching of the magnetization can be described by the so-called one-domain approximation, when the total magnetization vector M is taken as a main dynamic variable with fixed absolute value M. Then the total energy density, or the anisotropy energy E, is obtained from the spin-Hamiltonian H using a spin coherent state n) chosen along the direction n [332,333] ... 

The research group of Th.W. Hansch succeeded in 2002 to trap for the first time cold atoms in such an optical lattice. They cooled at first the atoms below the critical temperature fort BE condensation. Then the well depth of the optical lattice was increased. This transferred the coherent state of the atoms in the free BEC, where all atoms are in the same state i.e. described by the same wavefunction and are therefore not distinguishable, into the incoherent Mott state, where each atom sits on its separate location and can be therefore distinguished from the other atoms. Decreasing the well depth brings the atoms again back into the coherent BEC state. Just by changing the well depth of the optical lattice switches the atomic ensemble from a coherent into an incoherent state and back [1204]. 

Time instant (s) Coherence vector Switch states [m3 m2 "ill Detected mode TauTt... 

Figure Bl.14.9. Imaging pulse sequence including flow and/or diflfiision encoding. Gradient pulses before and after the inversion pulse are supplemented in any of the spatial dimensions of the standard spin-echo imaging sequence. Motion weighting is achieved by switching a strong gradient pulse pair G, (see solid black line). The steady-state distribution of flow (coherent motion) as well as diffusion (spatially...

Figure 6.2 Steering of photochemical reactions by coherent control of ultrafast electron dynamics in molecules by shaped femtosecond laser pulses. Ultrafast excitation of electronic target states in molecules launches distinct nuclear dynamics, which eventually lead to specific outcomes of the photochemical reaction. The ability to switch efficiently between different electronic target channels, optimally achieved by turning only a single control knob on the control field, provides an enhanced flexibility in the triggering of photochemical events, such as fragmentation, excited state vibration, and isomerization.

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

It is possible to build pulsed versions of the vacuum oscillators that can have variable pulsewidths and separations. The difficulty is in maintaining phase coherence between pulses. Solid-state sources may be switched to provide pulses, but the lower output powers limit the spectroscopist to selective pulses in many cases. As techniques become more advanced, pulse generation will become more and more common in near-millimeter band spectrometers. For the purposes of this chapter, however, we will limit our attention to CW sources. 

If at time zero, after the field has been switched off, the system is found in a state with nonvanishing coherences, oy (z 7), Eqs (18.43b,c) tell us that these coherences decay with the dephasing rate constant k. k was shown in turn to consist of two parts (cf. Eq. (10.176) The lifetime contribution to the decay rate of Oy is the sum of half the population relaxation rates out of states z and j, in the present case for 012 and <721 this is (l/2)( 2 i + 1 2)- Another contribution that we called pure dephasing is of the form (again from (10.176)) Zi 2C(0)(K — 22) - system operator that couples to the thermal bath so that — V22... 

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