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Physical Review Letters

Response of a Two-Level System Driven by Two Strong Fields

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

Published May 20, 1996• 45 citations
Publisher

Abstract

The absorption and dispersion response of a driven NMR two-level system in diamond is investigated using Raman heterodyne technique for which both pump and probe fields are strong. Up to 11 multiphoton resonances in dispersion and up to three-photon gain without inversion in absorption are observed. These gain features can be attributed to inversion between dressed states. Futhermore, a gain feature for which there is no inversion in either bare or dressed states is observed. The results are in good agreement with calculations.

DOI
10.1103/physrevlett.76.3943

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Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
The absorption and dispersion response of a driven NMR two-level system in diamond is investigated using Raman heterodyne technique for which both pump and probe fields are strong. Up to 11 multiphoton resonances in dispersion and up to three-photon gain without inversion in absorption are observed. These gain features can be attributed to inversion between dressed states. Futhermore, a gain feature for which there is no inversion in either bare or dressed states is observed. The results are in good agreement with calculations.
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.
This thesis studies the interaction between two-and three-level systems and strong, coherent radio-frequency (rf) electrom agnetic fields.The investigations were carried out in both the frequency domain, where steady state properties are examined, and the time domain, where transient behaviours are studied.The two-and three-level systems studied arise from the nuclear spin I = 1 triplet within the 3 A ground state of the nitrogen-vacancy (N-V) centre in diamond.The nuclear magnetic resonance (NMR) is detected optically using a coherent optical-rf double resonance Raman heterodyne technique.Owing to the unique features of both the nuclear spin triplet and the detection technique, many interesting experimental results have been obtained.The thesis is comprised of four parts.Part 1 includes Chapters 1 to 3, which provides introductory accounts.The two-level system concept and associated theoretical treatments in the density matrix formalism are introduced in Chapter 1.The theory is given in a very general form and is developed later in relevant chapters for specific situations.Chapter 2 gives an introduction to the N-V centre and its electronic and hyperfine energy levels.The Raman heterodyne technique and the experimental details are described in Chapter 3.In Part 2, consisting of Chapters 4 and 5, the nuclear magnetic transition of interest is characterized.Chapter 4 describes various coherent transient observations including nutation, free-induction-decay (FID), spin echo, spin locking, delayed FID, and rotary echo, from which important parameters such as the transition strength, population decay time T 1? and dephasing time T2 can be deduced.The dependence of these parameters upon the wave function mixing due to the level anti-crossing is discussed in Chapter 5.Part 3 is the most significant part of the thesis and consists of Chapters 6 to 9. In these chapters the interaction of a two-and three-level system with electromagnetic fields are studied in the frequency domain using pump-probe spectroscopy.This technique involves driving the systems with a strong (pump) field and monitoring it with a separate (probe) field.The absorption and dispersion profiles of a driven two-level system probed by a weak field are discussed in Chapter 6. Topics include the dynamic "Stark" effect and amplification without inversion.When the probe intensity is increased from weak to strong, multiphoton transitions and multiphoton gain without inversion are observed.These effects are described in Chapter 7. When the pump and probe fields interact separately with two transitions which share one common level the two-level system is extended to a three-level one.The power broadening of the Autler-Townes spectrum in such a three-level system is the topic presented in Chapter 8. Chapter 9 considers the case where there are two strong fields and a weak probe field.The discussion is in terms of the dressed state picture and it is shown that the dressed state can be also dressed.Experimental results of the transient nutation in dressed states are presented in part 4 which consists of Chapter 10.The dressed states transition strength is determined for the first time experimentally.Finally, Chapter 11 presents a summary of this thesis.
This paper reports on experimental investigations of absorption, dispersion, and amplitude profiles of the Autler-Townes doublet in a ssV-shaped three-level system where the probe field intensities varied from weak to strong. The experiments were carried out on the ground-state hyperfine transitions of the nitrogen-vacancy color center in diamond using the Raman heterodyne technique, a sensitive optically detected magnetic resonance technique. A strong pump field is on resonance with the Iz{\mathit{I}}_{\mathit{z}}Iz​=\ensuremath{\Vert}0〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 transition at 4.7 MHz and the resultant Autler-Townes profiles are probed with a separate field scanning through the Iz{\mathit{I}}_{\mathit{z}}Iz​=\ensuremath{\Vert}0〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}-1〉 transition at 5.4 MHz. As the probe power increases the absorptive profile of the Autler-Townes doublet becomes saturated and power broadened and the two components overlap constructively. In contrast, the inner parts of the two dispersive doublet components interfere destructively due to a \ensuremath{\pi} phase difference. The amplitude profile has an anomalous line shape at high probe intensity due to the different saturation behaviors of the absorptive and dispersive components. The experimental profiles are in good agreement with theoretical profiles calculated by solving the equation of motion of the density matrix under the steady-state limit.
Driven two-level atoms are shown to exhibit strong, resonantly enhanced, two-photon gain. This gain, unlike that observed in nonlinear mixing processes, is not constrained by a phase-matching condition involving the pump beam. Physically, the gain can be associated with inverted two-photon transitions between dressed states or multiphoton stimulated Raman scattering, and it may be useful in the realization of a two-photon laser. Comparison with the well-known single-photon gain found in the same system is made.
It is well known that driven two-level atoms can exhibit optical amplification.1 This fact has led to the recent demonstration of single-photon lasing in cell and atomic-beam type ensembles of two-level atoms.2 We show that the same simple two-level system can also be utilized as a two- or more-photon amplifying medium. The underlying physics can be understood in terms of the atom field dressed-state picture. When driven by a field detuned from the atomic resonance, significant population inversion between the dressed-state doublets can be created. In the dressed picture, single-photon lasing occurs between inverted sublevels of adjacent dressed-state doublets. Transitions between nonadjacent doublets are still inverted, but require two or more photons. In the degenerate case, the multiphoton emission frequencies differ from the single-photon emission frequency and can hence be selectively enhanced using an optical cavity. Due to the peculiar structure of dressed levels, the multiphoton emissions are all connected through near resonant intermediate states. The multiphoton emissions can also be viewed as a stimulated hyper-Raman scattering of successively higher order.