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Physical Review Letters

Dressed State Nutation and Dynamic Stark Switching

Changjiang Wei, Neil B. Manson, John P. D. Martin

Published Feb 13, 1995• 21 citations
Publisher

Abstract

Using Raman heterodyne detected nuclear magnetic transition in diamond we have observed dressed state nutation for two situations: (i) pulsed probe + cw pump and (ii) cw probe + pulsed pump. The dressed state Rabi frequencies are measured for the first time and found to have a $sin\ensuremath{\theta}$ and $cos\ensuremath{\theta}$ dependence ($\ensuremath{\theta}$ is a function of pump intensity and detuning). A simple consideration based on the dressed state model gives a satisfactory account of the observed dependence. When a 90\ifmmode^\circ\else\textdegree\fi{} phase shift is introduced, spin locking and strong oscillations are observed.

DOI
10.1103/physrevlett.74.1083

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Using Raman heterodyne detected nuclear magnetic transition in diamond we have observed dressed state nutation for two situations: (i) pulsed probe + cw pump and (ii) cw probe + pulsed pump. The dressed state Rabi frequencies are measured for the first time and found to have a sin\ensuremathθsin\ensuremath{\theta}sin\ensuremathθ and cos\ensuremathθcos\ensuremath{\theta}cos\ensuremathθ dependence (\ensuremathθ\ensuremath{\theta}\ensuremathθ is a function of pump intensity and detuning). A simple consideration based on the dressed state model gives a satisfactory account of the observed dependence. When a 90\ifmmode^\circ\else\textdegree\fi{} phase shift is introduced, spin locking and strong oscillations are observed.
In this paper we present a theoretical study of the time-dependent probe response in the presence of a strong pump field in a three-level pump-probe configuration. Two situations are investigated: a cw pump with a pulsed probe field and a pulsed pump with a cw probe field. The results are explained as dressed-state nutation and nutation by dynamic Stark switching. Dressed-state quantum beats are also an important feature for both situations. Furthermore, when a 90\ifmmode^\circ\else\textdegree\fi{} phase shift after a $\ensuremath{\pi}∕2$ period is introduced in the pulsed probe field, there is a spin locking in the dressed-state transition. Our results give a satisfactory theoretical account of a previous experimental observation [Wei et al., Phys. Rev. Lett. 74, 1083 (1995)].
The paper reports on experimental investigations of absorption and dispersion profiles of a strongly driven hyperfine transition at various pump field intensities and detunings when probed by a weak field. The transition lies at 5.4 MHz and corresponds to the Iz{\mathit{I}}_{\mathit{z}}Iz​=0\ensuremath{\leftrightarrows}-1 nuclear magnetic transition within the electron spin singlet of the 3^{3}3A ground state of the nitrogen-vacancy (NV) center in diamond. The inhomogeneous linewidth of the transition is 8 kHz whereas the homogeneous linewidth is 2.7 kHz, which is a factor of 3 larger than that limited by the population relaxations. The absorption and dispersion are obtained using Raman heterodyne detection, a coherent optically detected magnetic-resonance technique. Measurements are performed in a situation where there is an anticrossing of the ground-state electron-spin levels, as this leads to an enhancement of the hyperfine transition strengths and the optical sensitivity. Weak probe fields with Rabi frequency 0.6 kHz could then be used. The absorption and dispersion profiles were recorded for on-resonance pump fields of various strengths with Rabi frequencies of 0, 2.1, 3.7, 6.6, 11.8, and 21 kHz. In addition, the responses were recorded for an off-resonance field with a Rabi frequency of 55 kHz and detunings between -40 and +40 kHz. The corresponding response of an idealized driven two-level system has been calculated using an established density-matrix equation of motion formalism.When normalized to the profiles with no driving field, the calculated and experimental profiles are in excellent agreement. The nitrogen-vacancy system provides a very clear experimental illustration of a driven two-level system and some aspects are highlighted. For on-resonance pumping, the dispersion profile consists of a positive and a negative absorptionlike peak separated by twice the pump Rabi frequency. The peaks correspond to a significant signal strength (index of refraction) whereas at the frequency of the peaks in dispersion, the absorption is zero. The corresponding absorption profile consists of two dispersionlike features separated by twice the pump Rabi frequency, and between the two features there is negative absorption or gain. For off-resonance pumping, there are again two features. For example, in absorption response, there is an absorption peak and an amplification peak symmetrically displaced from the pump frequency by the generalized Rabi frequency. In this off-resonance pumping situation, it is pointed out that gain occurs where there is inversion in the dressed state whereas gain for the on-resonance pumping situation is achieved without population inversion in either the bare or dressed state.
We report on experimental measurements of transition strengths for spectral components associated with a driven two-level atom. The measurements involve time- and frequency-domain techniques and are performed in nuclear magnetic transitions of a nitrogen-vacancy colour centre in diamond using the optical Raman heterodyne method. The transition strengths are shown to depend on the characteristics of the driving field in a way readily accounted for by the dressed state formalism and the data provide an experimental confirmation of some elementary expressions frequently used for dressed states.
Optical nutation under Raman excitation accompanied by considerable (up to inverted) population changes was observed. The Raman-active 6P1/2–6P3/2 transition of thallium atoms was excited by picosecond pulses of a dye and an Nd : YAG laser. Transition polarization and upper level population were probed by delayed pulses at a fixed time by means of coherent Raman scattering and third harmonic generation schemes, respectively. Optical nutation manifested itself in corresponding changes of anti-Stokes and third harmonic signal energies as functions of the product of the pump pulses energies. As a result of the a.c. Stark shift, the nutation picture strongly depended on the sign of wavenumber detuning from the transition wavenumber. Copyright © 2000 John Wiley & Sons, Ltd.
The authors study the phenomenon of coherent Raman beats in 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ using a CO2{\mathrm{O}}_{2}O2​ laser and Stark switching. In particular, a three-level system in which the two upper levels always remain split by a few MHz is prepared by switching the transitions into resonance with a short Stark pulse whose bandwidth is large enough to coherently excite both transitions. When one of the coherently excited levels remains in resonance with the laser after the Stark pulse, this system exhibits a qualitatively new effect which has not been seen heretofore. For Stark shifts on the order of the upper-state splitting or smaller, the Raman beat is amplitude modulated at a frequency related to the optical nutation frequency. This is interpreted as being due to an interaction between the two-photon coherent Raman beat process and a single-photon optical nutation process which occurs simultaneously. Numerical calculations as well as a simple analytic model are presented to support this interpretation. By reducing the laser power, one can make the modulation of the Raman beat disappear. From the Raman signal in this regime the permanent electric dipole moment of 15N^{15}\mathrm{N}15NH3{\mathrm{H}}_{3}H3​ in an excited vibrational state is determined and the Raman beat decay rate measured. By comparing the latter result with a delayed optical nutation measurement we show that phase-changing collisions are negligible for the transition studied.
Raman-heterodyne-detected paramagnetic resonance has been used to study the level anticrossing in the 3^{3}3A state of the N-V defect in diamond. The electron-paramagnetic-resonance (EPR) frequencies are well accounted for by a triplet-spin Hamiltonian. Comparison of the EPR spectra with the calculated transition dipole strengths indicates that optical pumping determines, to a large extent, the Raman-heterodyne-signal intensity. Spin alignment in the 3^{3}3A ground state under optical pumping leads to the collapse of the EPR signal at the level anticrossing, where the population is equalized due to the mixing of the spin states. This is substantiated by transient nutation and spin-echo measurements, from which the dipole moment and dephasing time are examined. Laser detuning within the 638-nm zero-phonon line shows that the Raman signal is only detectable when the laser frequency is tuned to the low-energy part of the optical line.