Adiabatic passage

To understand many NMR phenomena we must recognize that the rate at which resonance is approached can be quite important. A very slow change of magnetic field or frequency is called adiabatic, and the adiabatic theorem tells us that if the rate of change is slow enough that 

M remains aligned with Beff. Far from resonance, Bcff = B0 (see Eq. 2.52), and M is, at equilibrium, aligned with B0. If the value of either B0 or co is varied under 

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The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

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X. Chen, 1. Lizuain, A. Ruschhaupt, D. Gudry-Odelin, and J. G. Muga, Shortcut to adiabatic passage in two- and three-level atoms. Phys. Rev. Lett, 105(12) 123003—123006(2010). 

A. del Campo, M. M. Rams, and W. H. Zurek. Assisted finite-rate adiabatic passage across a quantum critical point exact solution for the quantum Ising model. Phys. Rev. Lett., 109(11) 115703-115707(2012). 

J. Zhang, J. H. Shim, 1. Niemeyer, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, and D. Suter. Experimental implementation of assisted quanmm adiabatic passage in a single spin. Phys. Rev. Lett., 110(24) 240501—240505(2013). 

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N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann. Laser-induced population transfer by adiabatic passage techniques. Annu. Rev. Phys. Chem., 52 763-809(2001). 

T. Cheng, H. Darmawan, and A. Brown. Stimulated Raman adiabatic passage in molecules the effects of background states. Phys. Rev. A, 75(1) 013411-013421(2007). 

PIECEWISE ADIABATIC PASSAGE IN POLARIZATION OPTICS AN ACHROMATIC POLARIZATION ROTATOR... 

Coherent excitation of quantum systems by external fields is a versatile and powerful tool for application in quantum control. In particular, adiabatic evolution has been widely used to produce population transfer between discrete quantum states. Eor two states the control is by means of a varying detuning (a chirp), while for three states the change is induced, for example, by a pair of pulses, offset in time, that implement stimulated Raman adiabatic passage (STIRAP) [1-3]. STIRAP produces complete population transfer between the two end states 11) and 3) of a chain linked by two fields. In the adiabatic limit, the process places no temporary population in the middle state 2), even though the two driving fields - pump and Stokes-may be on exact resonance with their respective transitions, 1) 2)and... 

The discretized adiabatic procedure, and its analog with STIRAP, is but one possibility for achieving broadband response of an optical device. An alternative, which we discuss, relies on the analogy between the Jones vector description of an optical beam and the two-state time-dependent Schrodinger equation (TDSE). This equation has two commonly used solutions. One is rapid adiabatic passage (RAP), produced by swept detuning (a chirp), and the other is Rabi oscillations, specifically a pi pulse. The RAP has theoretical connection with STIRAP, but the pi pulses have no such connections. We describe application of a procedure that has been used to extend the traditional pi pulses to broadband excitation. This can accomplish the present goal of PAP, under complementary conditions. 

E. A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro. Piecewise adiabatic passage with a series of femtosecond pulses. Phys. Rev. Lett., 99(3) 033002 (2007). 

N. V. Vitanov, K.-A. Suominen, and B. W. Shore. Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage. J. Phys. B, 32(18) 4535 546 (1999). 

B. Torosov, S. Guerin, and N. V. Vitanov. High-fidehty adiabatic passage by composite sequences of chirped pulses. Phys. Rev. Lett., 106 233001 (2011). 

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