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Physical Review A

Experimental investigations of the absorption and dispersion profiles of a strongly driven transition: Two-level system with a weak probe

Changjiang Wei, Neil B. Manson

Published Jun 1, 1994• 39 citations
Publisher

Abstract

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 ${\mathit{I}}_{\mathit{z}}$=0\ensuremath{\leftrightarrows}-1 nuclear magnetic transition within the electron spin singlet of the $^{3}$A 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.

DOI
10.1103/physreva.49.4751

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Experimental investigations of absorption and dispersion profiles of a strongly driven transition:ssV-shaped three-level system with a strong probe

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Raman heterodyne detected magnetic resonance of the nitrogen-vacancy centre in diamond

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This thesis describes the Raman heterodyne detection of magnetic resonance in the ³A ground state of the nitrogen-vacancy C'-1· V) centre in diamond. The recently developed theory of Raman heterodyne spectroscopy was tested and compared with the spectra measured on the N-V centre. Among those results, the electron-nuclear double resonance (ENDOR), nuclear-nuclear double resonance (double NMR), Autler-Townes effect, coherence transfer and Zeeman quantum beat were observed for the first time using such techniques. Raman heterodyne techniques were also used to investigate the level anticrossing, hyperfine and nuclear quadrupole interactions, and spin relaxations of the N-V centre with high sensitivity and precision. This thesis is comprised of three parts. Part one includes Chapters 1 to 3, providing introductory accounts. Chapter l is an introduction to the N-V colour centre, which describes the defect configuration, the spin Hamiltonian and the calculations of energy levels and wave functions of the ³A ground state. Chapter 2 briefly describes the theory of Raman heterodyne spectroscopy - a coherent optical radio-frequency (RF) double resonance technique, in particular the Raman heterodyne signals at weak and intense RF fields. Chapter 3 deals with experimental details and techniques utilized in the studies. Part two consists of Chapters 4 and 5, where the Raman heterodyne theory is compared with experimental results. Chapter 4 presents the Raman heterodyne detected nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) lineshapes compared with theoretical results at various RF power levels, laser intensities and laser frequencies within the 6380A zero-phonon line. The double resonance spectra obtained by Raman heterodyne techniques are discussed in Chapter 5, where attention is paid to the analysis of their spectral profiles depending on the detection scheme. The application of Raman heterodyne techniques to the studies of magnetic resonance of the N-V centre is described in part three, consisting of Chapters 6 to 9. The EPR measurements are described in Chapter 6, which were used to study various interactions near the level anticrossing, in particular the spin alignment. The hyperfine and nuclear quadrupole interactions probed by the NMR, ENDOR and hole burning measurements are described in Chapter 7. From these measurements, the hyperfine and quadrupole parameters in the spin Hamiltonian were fully determined. Chapter 8 deals with the Autler-Townes effect in the NMR and EPR transitions. By measuring the Autler-Townes spittings, the magnitudes of matrix elements of the NMR transitions were examined and compared. Chapter 9 presents the coherent spin transient properties, including nutations, echoes, Zeeman beating and coherence transfer. The dephasing time and homogeneous linewidths of the NMR and EPR transitions were then determined from the echo measurements. Finally, the thesis is summarized in Chapter 10.

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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 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.
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.
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.
Quantum systems driven by strong oscillating fields are the source of many interesting physical phenomena. In this work, we experimentally study the dynamics of a two-level system of a single spin driven in the strong-driving regime where the rotating-wave approximation is not valid. This two-level system is a subsystem of a single nitrogen-vacancy (NV) center in diamond coupled to a first-shell 13C^{13}\mathrm{C}13C nuclear spin at a level anticrossing point. This near degeneracy occurs in the ${m}_{s}=\ifmmode\pm\else\textpm\fi{}1$ manifold of the electron spin when the energy level splitting between the ${m}_{s}=\ensuremath{-}1$ and +1+1+1 states due to the static magnetic field is $\ensuremath{\approx}127$ MHz and thus equal to the splitting due to the 13C^{13}\mathrm{C}13C hyperfine interaction. The transition frequency of this electron spin two-level system in a static magnetic field of 28.9 G is 1.7 MHz and it can be driven only by the component of the radio-frequency (RF) field along the NV symmetry axis. Electron spin Rabi frequencies in this system can reach tens of MHz even for moderate RF powers. The simple sinusoidal Rabi oscillations that occur when the amplitude of the driving field is small compared to the transition frequency evolve into complex patterns when the driving field amplitude is comparable to or greater than the energy level splitting. We observe that the system oscillates faster than the amplitude of the driving field and the response of the system shows multiple frequencies.
We present the results of an experimental and theoretical study of the gain (or absorption) experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3s → 3p atomic transition. The probe-transmission spectrum includes three distinct features that result from the modification of the atomic-level structure by the ac-Stark effect. Two of these features can lead to amplification of the probe wave. We measured the dependence of the probe spectrum on the detuning of the pump beam from resonance and on the pressure of a helium buffer gas. The experimentally obtained spectra are in good agreement with the predictions of a theoretical model based on the solution of the density-matrix equations of motion for a two-level atom and including the effects of Doppler broadening. The maximum gain measured in these experiments occurs at one of the Rabi sidebands and leads to a 38-fold increase in the intensity of the probe wave. Under some experimental conditions, we also observed two additional resonances, which are due to stimulated Raman scattering involving the sodium ground-state hyperfine levels.
This thesis describes the Raman heterodyne detection of magnetic resonance in the ³A ground state of the nitrogen-vacancy C'-1· V) centre in diamond. The recently developed theory of Raman heterodyne spectroscopy was tested and compared with the spectra measured on the N-V centre. Among those results, the electron-nuclear double resonance (ENDOR), nuclear-nuclear double resonance (double NMR), Autler-Townes effect, coherence transfer and Zeeman quantum beat were observed for the first time using such techniques. Raman heterodyne techniques were also used to investigate the level anticrossing, hyperfine and nuclear quadrupole interactions, and spin relaxations of the N-V centre with high sensitivity and precision. This thesis is comprised of three parts. Part one includes Chapters 1 to 3, providing introductory accounts. Chapter l is an introduction to the N-V colour centre, which describes the defect configuration, the spin Hamiltonian and the calculations of energy levels and wave functions of the ³A ground state. Chapter 2 briefly describes the theory of Raman heterodyne spectroscopy - a coherent optical radio-frequency (RF) double resonance technique, in particular the Raman heterodyne signals at weak and intense RF fields. Chapter 3 deals with experimental details and techniques utilized in the studies. Part two consists of Chapters 4 and 5, where the Raman heterodyne theory is compared with experimental results. Chapter 4 presents the Raman heterodyne detected nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) lineshapes compared with theoretical results at various RF power levels, laser intensities and laser frequencies within the 6380A zero-phonon line. The double resonance spectra obtained by Raman heterodyne techniques are discussed in Chapter 5, where attention is paid to the analysis of their spectral profiles depending on the detection scheme. The application of Raman heterodyne techniques to the studies of magnetic resonance of the N-V centre is described in part three, consisting of Chapters 6 to 9. The EPR measurements are described in Chapter 6, which were used to study various interactions near the level anticrossing, in particular the spin alignment. The hyperfine and nuclear quadrupole interactions probed by the NMR, ENDOR and hole burning measurements are described in Chapter 7. From these measurements, the hyperfine and quadrupole parameters in the spin Hamiltonian were fully determined. Chapter 8 deals with the Autler-Townes effect in the NMR and EPR transitions. By measuring the Autler-Townes spittings, the magnitudes of matrix elements of the NMR transitions were examined and compared. Chapter 9 presents the coherent spin transient properties, including nutations, echoes, Zeeman beating and coherence transfer. The dephasing time and homogeneous linewidths of the NMR and EPR transitions were then determined from the echo measurements. Finally, the thesis is summarized in Chapter 10.