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Probing an Excited-State Atomic Transition Using Hyperfine Quantum

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Probing an Excited-State Atomic Transition Using Hyperfine Quantum Probing an Excited-State Atomic Transition Using Hyperfine Quantum Beat Spectroscopy C. G. Wade,∗ N. Sibali´c,J.ˇ Keaveney, C. S. Adams, and K. J. Weatherill Joint Quantum Centre (JQC) Durham-Newcastle, Department of Physics, Durham University, South Road, Durham, DH1 3LE, United Kingdom (Dated: October 10, 2018) We describe a method to observe the dynamics of an excited-state transition in a room temperature atomic vapor using hyperfine quantum beats. Our experiment using cesium atoms consists of a pulsed excitation of the D2 transition, and continuous-wave driving of an excited-state transition from the 6P3=2 state to the 7S1=2 state. We observe quantum beats in the fluorescence from the 6P3=2 state which are modified by the driving of the excited-state transition. The Fourier spectrum of the beat signal yields evidence of Autler-Townes splitting of the 6P3=2, F = 5 hyperfine level and Rabi oscillations on the excited-state transition. A detailed model provides qualitative agreement with the data, giving insight to the physical processes involved. u I. INTRODUCTION | i e+ Excited-state transitions in atomic systems are finding an e | i ¯hΩ increasing range of applications including quantum infor- | i ¯hωb e− e0 |e0 i mation [1], optical filters [2], electric field sensing [3{5] | i | i and quantum optics [6, 7]. They are also used for state lifetime measurements [8], frequency up-conversion [9], g g the search for new stable frequency references [10, 11] and | i | i multi-photon laser cooling [12]. However excited-state | transitions are inherently more difficult to probe than | ) ) ω ω ground-state transitions, especially if the lower state is ( ( short-lived. It is possible to probe an excited-state tran- |F |F sition directly if the dipole moment is large enough [13], but more commonly excited-state character is observed + by mapping onto ground-state transitions using electro- ωb Ω ω− ω magnetically induced transparency (EIT) in a ladder Frequency Frequency configuration. Using EIT it is possible to probe even relatively weak excited-state transitions, such as those to highly excited Rydberg states [14{16]. Nanosecond timescales have also been probed, effectively `freezing Fluorescence Time Fluorescence Time out' the motion of thermal atoms [17]. EIT involving Rydberg states has paved the way to FIG. 1. (Color Online) Toy model of our experiment. Left: recent advances in non-linear and quantum optics [6] as Atoms prepared in a superposition of closely spaced excited the strong interactions among the Rydberg atoms lead states e and e0 demonstrate quantum beats at a frequency j i j i to large optical non-linearities, even at the single-photon corresponding to the difference in their energies. Right: Driv- ing an excited-state transition splits state e into two dressed level [7, 18, 19]. In room temperature Rydberg gases, the + j i states e and e− and the dynamics of the excited-state atomic interactions can lead to a non-equilibrium phase transitionj i are writtenj i into the quantum beats. We show the transition [20] and evidence for strong van der Waals in- level scheme (top), the Fourier spectrum, (!) , of the flu- teractions has been observed [21]. Despite the consider- orescence (middle) and the time-dependentjF fluorescencej into arXiv:1408.3506v2 [physics.atom-ph] 6 Oct 2014 able successes of ladder EIT, there is a particular class an appropriately chosen polarization mode (bottom). The of energy level schemes for which ladder EIT cannot be Fourier spectra are calculated by taking the magnitude of the observed in a Doppler-broadened medium. Specifically, Fourier transform of the fluorescence signals. when the upper transition wavelength is longer than the lower (`inverted-wavelength' system) [22, 23], the trans- parency window is absent as it is smeared out by velocity In this paper we make novel use of hyperfine quan- averaging. tum beats [24, 25] to probe the excited-state transition dynamics of an `inverted-wavelength' ladder system in a thermal vapor. We find strong evidence for both Rabi oscillations and sub-Doppler Autler-Townes splitting. ∗ [email protected] The paper is organized as follows: In Section II we con- 2 struct a toy model of our experiment, giving an overview (a) F 00 = 4 7S (b) of the physics involved. Section III details our experi- 1/2 1469 nm (CW) mental procedure and in Section IV we present results in 1469 nm Vertical Polarizer both the time-domain and the frequency domain. Sec- Detector tion V outlines a computer model that we developed to Pulse Polarizer understand the signals, which we compare to the data in band- Photon Section VI. The model yields good qualitative agreement width Counter Vapor which allows us to interpret features that we observe in 852 nm Cell Bandpass the frequency domain. 6P3/2 Filter F 0 = 5 Vertical Polarizer II. PRINCIPLE OF PERTURBED QUANTUM F 0 = 4 Pockels Cell BEATS IN A LADDER SYSTEM F 0 = 3 Horizontal Polarizer In this section we outline a toy model of our ladder sys- 852 nm F = 4 6S1/2 tem which includes the minimum possible complexity 852 nm to illustrate the physical principle (Figure 1). The toy model considers a zero-velocity atom with ground state jgi, an intermediate excited state jei and an upper ex- FIG. 2. (Color Online) (a) Level scheme of our experiment: 0 A short pulse of light excites several states in the 6P3=2 cited state jui. There is also a reference state je i which manifold and a CW laser drives an excited-state transition is close in energy to jei. The transition from jgi ! jei 6P3=2 F = 5 7S1=2 F = 4 (b) Schematic of experiment: Ver- is driven by a short pulse whilst a continuous wave (CW) tically polarized! beams counter-propagate through a cesium laser drives the excited-state transition from jei ! jui. vapor cell and fluorescence from the D2 transition is detected For a sufficiently short excitation pulse the bandwidth with a single photon counter. exceeds the energy interval between jei and je0i, and a coherent superposition of the two states is prepared by the pulse. The dynamics of the excited-state transition To understand the effects of driving the excited-state are read out by measuring the fluorescence from states transition it is easiest to consider the dressed state pic- jei and je0i. ture (right hand column of Figure 1). CW driving of We begin our explanation by considering the simple the excited-state transition splits jei into two dressed + − case when the excited-state transition driving field is states, je i and je i, separated according to the Rabi switched off (left column of Figure 1). Once the co- frequency of the driving field, Ω. The original beat at herent superposition of states jei and je0i has been pre- frequency !b, is split into two distinct beats with fre- + − pared, the total fluorescence decays exponentially accord- quencies, ! = !b + Ω=2 and ! = !b − Ω=2. ing to the state lifetime. However, the fluorescence into Furthermore, a new beat frequency is introduced with an appropriately chosen mode, characterized by polar- frequency Ω. This beat frequency relates to Rabi oscilla- ization and propagation direction, is modulated by beat- tions with atoms cycling on the excited-state transition. ing [26]. These `quantum beats' represent interference We note that unlike the initial quantum beat, this cy- between the two different quantum pathways associated cling leads to a modulation of the total fluorescence, not with jei and je0i. The interference is erased if infor- just a particular polarization mode. The Fourier spec- mation regarding which pathway was taken is recovered trum, jF(!)j, includes all information regarding Autler- (e.g. spectroscopically resolving the fluorescence from Townes splitting of the state jei and Rabi oscillations each state). In our toy model the time-dependent fluo- on the excited-state transition, jei ! jui. The more rescence into a particular mode has the form of an expo- complicated form of the time-dependent fluorescence is nentially decaying envelope modulated by beating. The shown in the lower right panel of Figure 1. modulus of the Fourier transform of this time-dependent fluorescence, jF(!)j, allows us to read off the beat fre- quency (see middle row of Figure 1). States jei and je0i III. EXPERIMENT have energy ~!e and ~!e0 respectively, and the beat fre- quency !b = !e − !e0 corresponds to the difference in The simplified level scheme and experimental setup are energy. The visibility of the beats from a zero-velocity shown in Figure 2a and Figure 2b respectively. We use atom is set by a number of factors including the distri- cesium atoms in a vapor cell (length 2 mm) at room bution of the population between the two states and the temperature (19 ◦C). The ladder scheme comprises the 0 relative strengths with which the states couple to the se- 6S1=2 F = 4 state as the ground state, 6P3=2 F = 5 as the 00 lected fluorescence mode. In our experiment the visibility intermediate state and 7S1=2 F = 4 as the upper excited is limited by velocity averaging as well. state. The other 6P3=2 hyperfine states play the role of 3 F F F F F 8 F 0 0 0 0 0 0 = 3-5 = 3-4 = 4-5 = 3-5 = 3-4 (a) (b)= 4-5 (c) (d) 1 Magnitude of Normalized Fourier Transform 6 0.8 0.6 4 0.4 2 0.2 0 0 (e) (f) (g) (h) 4 0.25 0.2 Photon Count Rate3 (MHz) 0.15 2 0.1 1 0.05 0 0 0 20 40 0 20 40 0 200 400 0 200 400 Time (ns) Time (ns) Frequency (MHz) Frequency (MHz) FIG.
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