INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS J. Opt. B: Quantum Semiclass. Opt. 7 (2005) 109–118 doi:10.1088/1464-4266/7/4/004 Optical pumping and electromagnetically induced transparency in a lithium vapour

FMagnus1,ALBoatwright2,AFlodin3 and R C Shiell4

Department of Physics, University of Sussex, Falmer, Brighton BN1 9QH, UK

E-mail: [email protected]

Received 20 November 2004, accepted for publication 7 February 2005 Published 9 March 2005 Online at stacks.iop.org/JOptB/7/109 Abstract We report the first study of electromagnetically induced transparency (EIT) on the D1 and D2 lines of 7Li in a vapour cell. The effect of different polarizations, background gas pressures and experimental designs on the dark resonance are examined. It is found that EIT is more prominent on the D1 line than on the D2 line and is present at the D2 transition under incident orthogonal linearly polarized fields and parallel circularly polarized fields, butabsent for parallel linearly polarized fields and for orthogonal circularly polarized fields. It is shown that the contrast of the dark resonances can be affected by the presence of an inert background gas. An analysis of a further nine resonances observed at the D1 transition and three resonances at the D2 transition is presented.

Keywords: electromagnetically induced transparency, coherent population trapping, optical pumping, lambda systems, lithium (Some figures in this article are in colour only in the electronic version)

1. Introduction trapped, and so this phenomenon is called coherent population trapping, and where the transmission of the probe beam There has recently been increasing interest in the role that non- through the medium is observed to increase under these linear optical phenomena play within atoms and molecules [1]. conditions, this phenomenon is called electromagnetically These can be clearly demonstrated when two light fields are induced transparency (EIT). Applications of this process incident on an atom or molecule with three internal levels include lasing without inversion [2], the slowing down of light where effects such as saturation and optical pumping of a signals in dilute media by many orders of magnitude [3, 4], particular velocity class by a strong ‘pump’ laser beam can and the measurement of transition dipole moments (see [5] for be detected through the increased transmission or absorption such a measurement in the Li2 molecule). of a weak ‘probe’ laser beam that interrogates the same The theory that describes saturation, optical pumping velocity class of atoms. The presence of the two laser andcoherent population trapping for three-level systems that beams can also create quantum coherences within the atoms can interact with a bichromatic light field for a long time wherebyattwo-photon resonance an ‘uncoupled’ state exists is well understood. A typical three-level lambda system is such that the probability amplitudes for optical excitation shown in figure 1. We shall label the energy of the ith bare from each of its components due to the two light fields state (i.e. the energy in the absence of the laser fields) by exactly cancel each other. The population in this state is Ei and take the energy separation between states |i and | j − = ω 1 Present address: Blackett Laboratory, Imperial College of Science, to be Ei E j h¯ ij.Theatoms are irradiated by two Technology and Medicine, Prince Consort Road, London SW7 2BZ, UK. monochromatic laser fields (which are treated semiclassically) 2 Presentaddress: School of Chemistry,University of Nottingham,University of amplitude ε1 and ε2 andangular frequency ω1 and ω2.We Park,Nottingham NG7 2RD, UK. assume that the frequency of laser 1 is near resonant with the 3 Present address: Department of Physics, Uppsala University, SE-751 21 transition frequency ω ,thatlaser 2 is near resonant with ω , Uppsala, Sweden. 12 23 4 Author to whom any correspondence should be addressed. Present address: andthat the laser polarizations are such as to couple the lasers to Physics Department, Trent University, 1600 West Bank Drive, Peterborough, their respective transitions. It isconvenient to define the (small) ON, K9J 7B8,Canada. detunings of the lasers from resonance as 1 = ω1 − ω12

1464-4266/05/040109+10$30.00 © 2005 IOP Publishing Ltd Printed in the UK 109 FMagnus et al which was attributed to the leaky nature of the single  system present, and the dark resonances at the |Fg = 1→|Fe = 1 and the |Fg = 2→|Fe = 2 transitions demonstrated very similar amplitudes to each other. The dark resonance at the |Fg = 2→|Fe = 1 transition had the greatest contrast; this wasbecause this system was least ‘leaky’ (within five cycles 2 of spontaneous decay from the P1/2 state, only one of these would be to |Fg = 1, outside the  system). Studies on the effect of hyperfine structure in EIT observed in cascade systems have included those of McGloin et al [10] and Badger et al Figure 1. The  energy level configuration. [11]. In both these studies there was a significant dependence of the strength of the two-photon resonance peak upon the → → and 2 = ω2 − ω12.The two-photon resonance, or Raman incident laser polarization at the 5s 5p 5d transitions in resonance, condition then corresponds to 1 = 2. rubidium. In the former study, the ratios of the observed peak In particular, this model is a useful one with which to heights agreed with those calculated from transition dipole describe the effect of a bichromatic light field on the D matrix calculations. 2 transitions of the alkali atoms. For these atoms the S1/2 This work presents some results due to two incident laser electronic ground state is split into two levels due to hyperfine beams on a vapour of lithium atoms at both the 7Li D1 and interactions and a fine-structure component of the upper 2P D2 transitions, in the first study on this species. Lithium term is split into hyperfine components, one member of which is of general interest in atomic physics; in addition to being plays the role of state |2 in this model. In reality, however, asystem in which the effects of closely-spaced hyperfine the actual levels within the alkali atoms are more complicated states can be studied, it is the simplest of the alkalis, for than figure 1 would indicate—each hyperfine level comprises which very accurate atomic structure calculations can be several degenerate (in the absence of any external fields) MF performed [12]. A theoretical analysis of the behaviour of 2 states and, for the P3/2 levels of both lithium and potassium, dark resonances for atoms with upper-level structure in a high- the small hyperfine splitting (A =−3.06 MHz for 7Li and pressure buffer gas has been developed by Taˇıchenachev et al A = 6.06 MHz for 39K, for example [6]) raises the interesting [13], where the assumptions used correspond to buffer gas possibility of investigating the effect of very dense excited pressures significantly greater than used here. state hyperfine structure on the formation of trapping states at This paper is presented as follows. In section 2 we the D2 transitions. This structure can be expected to result in describe the experiment in which various configurations of significant deviations from theoretical predictions based solely laser polarization and beam geometry were used, in section 3 on an analysis of the simple system shown in figure 1. In this we present the spectra obtained by detecting the transmission paper we report and compare the presence (and absence) of of either the probe laser, or the pump and the probe EIT at the D1 and D2 transitions of lithium atoms in a vapour simultaneously, and in section 4 we present an analysis of the cell for the first time, and the effect of different experimental results and discuss their significance. conditions upon the spectral features. Previous experimental studies on the effects of hyperfine 2. Experimental details structure on EIT have investigated the spectroscopy of cesium, The lithium vapour cell consists of a stainless steel tube of rubidium and sodium in both  and cascade configurations. 3/4inchexternal diameter with glass windows at each end Stahler¨ et al [7] compared the visibility of the EIT peak and a single core heating element (Thermocoax) wrapped 85 2 at the D1 transitions in Rb (A( P1/2) = 121 MHz) and around the centre of the tube. The cable was wound in 2 the D2 transitions (A( P1/2) = 25 MHz), and observed a abifilar arrangement with an equal number of windings in significant increaseincontrast, and decrease in resonance both directions to reduce any induced magnetic field. A width, for the D1 system. Using a small magnetic field thermocouple is held near the centre of the tube and the tube is Nagel et al [8] have recorded the amplitude and FWHM of rigidly held at each end by water-cooled aluminium plates. | = , = the coherence formed between the states Fg 3 MFg 0 This ensures that lithium vapour does not reach and react | = , = and Fg 4 MFg 0 at the cesium D2 transition with with the glass windows, but necessarily means that the atomic | = , = | = circularly polarized light (i.e. with Fe 3 MFe 1 or Fe vapour is not in thermodynamic equilibrium. The cell has two , = | 4 MFe 1 playing the role of state 2 in this system). They gas inlets/outlets; one is connected to a capsule pressure gauge observed that as the carrier frequency and its 9.2 GHz sideband (Edwards CG3) and the other to a pumping station consisting 2 were simultaneously scanned across the P3/2 manifold and of a diffusion pump and a rotary backing pump. The cell can be detuned away from either of the upper states of the  system, pumped down to approximately 10−4 mbar and could be filled the amplitude of the dark resonance decreased. This was to apredetermined pressure with a buffer gas (argon, 99.998% consistent with transitions from one of the components of purity, BOC). | = , = 7 the uncoupled state to either the Fe 2 MFe 1 or the Inside the cell lithium in its natural abundance (93% Li, | = , =  6 Fe 5 MFe 1 state—i.e. a ‘leaky’ system exhibiting 7% Li) is placed on a molybdenum boat. Although the melting one-photon losses. Renzoni et al [9] investigated the evolution point of lithium is 180 ◦C, in our experience there are no visible of Zeeman coherences involved in different transitions within signs of melting at or above this temperature. We conclude the sodium D1 line by using σ +/σ − incident polarization. The that thesample is surrounded by a solid oxide or hydroxide |Fg = 1→|Fe = 2 transition displayed no dark resonance, layer which cracks upon heating and releases lithium vapour.

110 Optical pumping and electromagnetically induced transparency in a lithium vapour

Figure 2. (a) Crossed configuration for the experiments. The pump beam (laser 1) was scanned and the probe beam (laser 2) was detected. (b) Collinear configuration for the experiments with the polarizations arranged in the lin ⊥ lin configuration.

Atomic absorption profiles at the 7Li D1 and D2 transitions configuration (see figure 2). The diameter of each laser (centred at 446 800 and 446 810 GHz, as measured on an beam was 1–2 mm and the power in the pump beam was Advantest Q8326 wavemeter) are visible when the temperature approximately 40 times greater than the probe beam (see of the thermocouple reads between 400 and 500 ◦C. At these below for precise values). In the crossed configuration the temperatures the atomic number density in the middle of the states of polarization of the pump and probe lasers could be cell is expected to be ≈1012 cm−3 [14]. Whilst the precise set independently of each other and, due to the geometry of depthofeach absorption profile is observed to be highly this configuration, the transmission of the probe beam could temperature dependent, the overall shape is approximately always be selectively recorded. In general, in this case there Gaussian with width 4 GHz. This is consistent with a ground will be a small amount of mixing (less than 1%) of different state hyperfine splitting in 7Li of 803.5 MHz [15] and a Doppler polarization states in the resultant laser field in the interaction width of 3 GHz for each contributing transition. The D2 line region associated with the addition of the non-collinear electric of 6Li (with ground state hyperfine splitting of 226 MHz [15]) field vectors from each beam. However, to a very good level occurs within the same spectral region as the D1 line of 7Li, of approximation we use the same polarization labels as for the collinear case to describe the incident polarization in these and these transitions are expected to make a small contribution experiments. For selective detection of the probe beam in to the net absorption profile at 446 800 GHz. the collinear configuration the polarizations of the pump and The lasers used were single-mode external cavity diode probe beams were oriented in a lin ⊥ lin arrangement and a lasers in the Littrow configuration [16] in which the zeroth- polarizing beamsplitter cube was used, as seen in figure 2. orderbeam from the grating constitutes the laser output. We also present spectra from both beams with parallel linear Limited frequency tuning of these lasers without mode hops polarization, in which case the transmission of both beams was ≈ ( 1 GHz) can be accomplished by changing the voltage across recorded. apiezoelectric stack within the diode mount, thereby changing For all but one of the spectra shownhere, the pump laser the length of the external cavity.Toensure a single longitudinal was scanned across the frequency range of interest in a typical mode remained in common with both the external and internal time of 0.5 s and the transmission of the probe beam was cavity as the laser is tuned overabroader range (up to 10 GHz), recorded. This had the advantage that the features observed in thecurrent through the laser diode (Toshiba TOLD9225) was thespectra were on a flat background, instead of on a Doppler increased proportionally to the stack voltage using a simple profile, and this enabled more accurate assessments of peak amplifier circuit. heights. For the case of the collinear beam configuration with For these experiments two co-propagating laser beams parallel polarizations, the power of both beams was recorded, were passed through the vapour cell in two different andthe Doppler profile, of course, was then evident. configurations: with the pump and probe laser beams at a The linewidth of the diode lasers were initially determined small angle (3–4 mrad) to each other (the ‘crossed’ beam by heterodyning them on a fast photodiode (EOT ET-2030A) configuration) and also with the beams in a ‘collinear’ and the beat signal observed with a spectrum analyser (Hameg

111 FMagnus et al

(a) T

ΛP1 ΛD1 ΛP2 ΛD 2 0.53

F1 F2 V1 V2 F3 F4

0.52

0.51

6 4 2 0 −2 −4 Residuals (MHz) Transmission −6 −800 −400 0 400 800 Fitted pump frequency (MHz)

0.514 (b)0.535 (c) (d) 0.510 0.512 0.525 0.51 0.508

Transmission 0.508 0.506 0.515 −900 −800 −700 −100 0 100 700 800 900 Fitted pump frequency (MHz) Fitted pump frequency (MHz) Fitted pump frequency (MHz)

Figure 3. Probe transmission on the D1 line as a function of pump frequency in the collinear configuration and lin ⊥ lin polarization. (a) Complete spectral range, (b) enlargement of low-frequency peaks, (c) enlargements of structure near zero frequency, (d) enlargements of high frequency structure.

5012-2) with 40 ms sweep time. The resulting spectra with lower. The corresponding range of Rabi frequencies for the spans of 50 MHz demonstrated a peak of −3dBlinewidth of probe laser is from 28 × 106 to 11 × 106 rad s−1.Thesecan be less than 2 MHz, indicating that the linewidth of each laser compared with the width of each upper level due to its radiative was ≈1MHz,recorded in a 1 ms measurement time. A series lifetime, which is 37 × 106 rad s−1. of these spectra taken one minute apart resulted in a change The frequency axis has been calibrated by fitting a in beat frequency of 4 MHz per minute, indicating that the quadratic function to the interference fringes and setting frequency drift of each laser during a 0.5 s scan was 2–3 MHz. the spacing between the peaks labelled P1 and P2 to The probe (unscanned) laser was placed near the centre 1607 MHz [6], which was consistent with the frequency of the Doppler-broadened absorption profile at the 7Li D1 difference determined from the coarse frequency calibration line or D2 line before each scan. Part of the pump laser determined solely by counting interference fringes. The beam was sent to an interferometer with path length difference abscissa values in this figure are relative to the central peak; of approximately 3.3 m. This enabled the spectrum to be note that positive frequencies correspond to the pump being put on a linear frequency scale and provided an absolute higher in frequency than the probe and vice versa. Below the calibration of the frequency difference of the pump laser across spectrum are displayed the residuals from the quadratic fitting a2GHz scan range to an accuracy of ≈60 MHz. More precise routine showing a slight systematic low-frequency sinusoidal calibration of the frequency difference was achieved by fitting difference between the fitted frequency and that corresponding a quadratic function to the interference fringes and setting to each fringe, which is probably attributable to the diode the spacing between two assigned features in the spectrum current and stack voltage being imperfectly scanned together. to values obtained from the literature [6, 16, 17]. Nevertheless, the quadratic fit (with only two parameters and an arbitrary offset) is good to better than 5 MHz over the 3. Results 1800 MHz scan range. The spectrum shows 11 different resonances in 7Li that 7 3.1. Spectra at the Li D1 transition can be explained in terms of subsystems of its energy level Figure 3 shows the probe transmission spectrum in the collinear structure. These results are similar to ones recently obtained by configuration with lin ⊥ lin polarization, as the pump laser is Wong et al [19] for resonances of the sodium D1 line and some scanned. The incident pump and probe powers are 4 mW and of their notation will be adopted here. The central transmission 110 µWrespectively in a 1.5 mm diameter beam, and no buffer peak labelled (T) is principally due to optical pumping and, to gas is present in the cell. For the allowed transitions within the alesser extent, saturation in a two-level subsystem when both D1 line, the pump intensity corresponds to a Rabi frequency lasers are resonant on the same transition. Due to Doppler × 6 −1 | = , = of 173 10 rad s for the (strongest) Fe 2 MFe shifting of the frequency of radiation seen by differentvelocity ± ↔| = , =± 2 Fg 1 MFg 1 transitions with electric dipole groups of atoms there are four possible subsystems involved, − − moment [18] of 1.4 × 10 29 Cm,and 71 × 106 s 1 for√ the shown infigure 4. The two peaks on either side of the weakest transitions with electric dipole moment a factor of 6 central peak labelled V1 and V2 result from optical pumping

112 Optical pumping and electromagnetically induced transparency in a lithium vapour

94

92

90

88 Transmission (%) π−pol'd

86 σ−pol'd

− 1000 − 500 0 500 1000 ν pump (MHz)

Figure 5. Probe transmission on the D1 line as a function of pump frequency in the crossed configuration, for parallel linear (labelled π)andparallel circularly polarized (labelled σ)incidentbeams. The top trace is shifted vertically upwards by 1% for ease of comparison, butthe traces otherwise are on the same scale. Figure 4. Thesubsystems responsible for each of the resonances of figure 3. The strong pump is denoted by a heavy arrow and the weak spontaneous emission from the excited state resulting in probe with a light arrow. The Fg and Fe total angular momentum quantum numbers of the ground and excited levels take the values of increased absorption of the probe. 1or2asshowninthetopleftofthis figure. Zeeman sublevels are Finally, there are two small peaks to the left of V1 and not shown. right of V2, separated by 460 MHz in the spectrum. Within experimental uncertainty, thisistwice the hyperfine splitting and saturation in a three-level V subsystem. Here, the lasers of the ground state of 6Li (natural abundance 7%) and these areresonant with transitions from a common ground state to are therefore due to transitions within the D2 line of this different excited states. These peaks differ in frequency from atom, which occurs within the same spectral region as the D1 the central peak by the hyperfine splitting of the two excited transitions of 7Li. states which is 91.8 MHz [6, 17]. For each of the peaks there Figure 5 shows two transmission spectra obtained using aretwo possible subsystems involved due to Doppler shifting, the crossed configuration with no buffer gaswhenthe beams one for each of the hyperfine ground states shown in figure 4. are vertically polarized, and when they are circularly polarized  / The transmission peaks and dips labelled P1 D1 and in the same sense. The incident pump and probe powers are  / P2 D2 are due to electromagnetically induced transparency 3.1 mW and 140 µWrespectively in a 2 mm diameter beam. and conventional optical pumping, respectively, in a three-level The top trace has been shifted vertically upwards by 1% for  subsystem. For each peak and dip there are two possible ease of comparison, but the traces are otherwise on the same contributing -subsystems for the two different common scale. These spectra show the same resonances as figure 3 excitedstates. The pump transfers population to the ground although the features are broader and less pronounced. The state from which the probe is exciting, resulting in increased four resonances labelled F1 to F4 in figure 3 that are due to absorption of the probe. However, at Raman resonance, where the single subsystems mentioned above have a characteristic the frequency difference of the two fields equals the ground intensity pattern for each of the two traces. We discuss this state hyperfine splitting of 803.5 MHz, the combined action further in section 4. of the pump and probe results in an eigenstate from which Figure 6(a) shows spectra for parallel circularly polarized excitationtothe upper state of the  system is not possible beams in the crossed configuration at different argon (see section 4). The population of this uncoupled state can be background gas pressures. Some of the traces are vertically further increased by spontaneous decay from the upper state, scaled as depicted in the figure, and all have been shifted and under the conditions typically found in a vapour cell the vertically for easy comparison. Therefore information about height of this peak is indicativeofboth the initial population the absolute transmission for each trace is not provided, of this state and its increase through optical pumping. although the heights of each spectral feature may be reliably The two outer pairs of shallow transmission dips, labelled compared. The traces demonstrate a systematic change in F1 to F4 in figure 3, are due to optical pumping in a four- both the optical pumping features and the EIT features as the level subsystem as shown in figure 4. Note that in contrast to pressure is monotonically varied. The capsule gauge used is the other spectral features shown in the spectra we present, accurate to ≈1mbar,anditcan be concluded that the optimal only one four-level subsystem contributes to each of these pressure for observation of the EIT peaks lies between 0 and well-resolved dips,whichmakesthemmost amenable to 1mbar,whilst the optical pumping peaks are most visible at quantitative analysis (see below). Each of these four features the lowest pressure reached. At a pressure of 1 mbar, and corresponds to the two laser beams being resonant with atemperature of 400 ◦C, the mean free path of gas atoms of transitions from different ground states to different excited diameter 1 Å is of the order of 2–3 mm, which is a typical states. The dips are therefore separated from the EIT peaks distance of travel during which the atoms are irradiated by the by the splitting of the upper hyperfine states. The strong laser beams. It may therefore be expected that collisions play pump transfers population to the other ground state through arolehere,and this is discussed in section 4.

113 FMagnus et al

(a) fields differ in frequency by the ground state hyperfine splitting. However, thedarkresonance disappears completely under parallel linear polarized fields which is not the case on the evacuated D1 line. Moreover, we have observed the EIT resonances to be present under orthogonal linear polarizations but absent under orthogonal circular polarizations. This behaviour will be discussed in section 4, below. Figure 8 shows probe transmission spectra, in the crossed Transmission (a.u.)

» 1 mbar ·5 configuration for parallel circularly polarized beams, over a similar range of background gas pressure to those shown in ·5 figure 6. The top trace corresponds to the lowest pressure, and » 1.5 mbar ·5 traces below to increased pressure. These spectra were taken − 500 0 500 1000 νpump (MHz) without the capsule gauge in place and therefore the absolute pressures are not presented. Some of the traces are scaled (b) as depicted in the figure, and all have been shifted vertically for easy comparison. The effect of background gas is seen to evacuated be qualitatively the same as was found for the D1 line. For no background gas the EIT peaks are barely visible in this crossed configuration and the optical pumping resonances are very clear. For increased argon pressure the EIT peaks become more pronounced, whereas the optical pumping resonances

Transmission (a.u.) diminish. Such spectra takenwith fields polarized linearly » 1 mbar ·5 in the same sense revealed no presence of EIT, even in the ·5 presence of argon background gas.

» 1.5 mbar ·5 4. Analysis and discussion − 500 0 500 1000 ν pump (MHz) 4.1. Theoretical background to EIT Figure 6. (a) Probe transmission in the crossed configuration for The coherent evolution of the three-level model system shown different argon gas pressures and parallel circular polarization at the in figure 1 can be determined exactly (within the rotating D1 transition. Some of the traces are vertically scaled as shown in wave approximation) either by solving the time-dependent the figure, and all are shifted vertically for easy comparison (see text). (b) As in (a), but for parallel linear polarization. Schrodinger¨ equation for the state vector of the system when irradiated by two laser fields, or, equivalently, by solving Forsmall amounts of background gas the EIT peaks the Liouville equation for the density operator [20]. The emerge strongly and they remain prominent for increased argon matrix elements of the density operator in a particular basis pressure up to approximately 1 mbar. At buffer gas pressures setthen give the relevant populations (diagonal elements) and above this they appear to decrease in contrast (there is very little coherences (off-diagonal elements) of the system. In fact, the transmission of any oftheprobe light at these pressures). Of system shown in figure 1 does not include any decay, either out particular interest is the reduced contrast of the dark resonance of the system (e.g. ionization, or fluorescence to other states) or with very low buffer gas pressure, and its disappearance at within the system (e.g. spontaneous decay to states |1 and |3, pressures >1.5mbar.Thisis discussed below. The optical or collisional decay between the states). The former process pumping dips generally show opposite behaviour to that of can be included within the state vector approach by adding a the EIT feature, and disappear almost entirely for pressures negative decay term to the equation of motion of the upper state, of 1 mbar and above. Figure 6(b) shows similar spectra resulting in an imaginary term in the Hamiltonian matrix [21] for linearly polarized light. The EIT peaks are less distinct and works because the subsystem remains in a pure quantum than for circularly polarized light but all features show the state [22]. In order to model decay within the system the same dependence as shown in figure 6(a) on background gas density matrix approach is more appropriate as it permits the pressure. system to evolve from a pure state to a mixed state, through the phenomenological addition of decay terms to the equations of 7 3.2. Spectra at the Li D2 transition motion of the density matrix elements. Figure 7 shows the transmission spectra from both pump and The absorption of a probe beam through a dielectric probe beams in the collinear configuration where the beams medium is then usually determined by relating the oscillating have parallel polarization. As discussed above, the hyperfine (complex) polarization vector of the medium, P˜(t),tothe 2 splitting of the P3/2 excited state is small and so the two laser oscillating (complex) electric field E˜(t) through the relation fieldscouple all the hyperfine excited states (Fe = 0, 1, 2, 3) ˜ ˜ simultaneously. Therefore, we do not see the resonances P(t) = ε0χ(ω)˜ E(t), (1) previously labelled (F) and (V) resolved, as on the D1 line. The centre peak is equivalent to the D1 (T) and (V) peaks, where χ(ω)˜ is the complex susceptibility. This relationship the two dips at ≈±800 MHz are equivalent to the Dand assumes that the (multilevel) atoms are in some sense at ‘steady (F) dips of the D1 line and again we see the clear presence state’ in thelaser field,which is often a good approximation for of electromagnetically induced transparency peaks when the atoms within a vapour cell when interrogated by a weak probe

114 Optical pumping and electromagnetically induced transparency in a lithium vapour

σ polarized (a) Transmission (a.u)

− 1000 − 500 0 500 1000 νpump (MHz)

(b) (c)

σ polarized π polarized Transmission (a.u) Transmission (a.u)

− 803 − 803 νpump (MHz) νpump (MHz)

Figure 7. (a): Transmission of both pump and probe beams at the D2 line as a function of pump frequency in the collinear configuration, in parallel circularly polarized fields. (b) and (c): Enlargements of the low-frequency feature for parallel circularly and linearly polarized beams, respectively.

with phases of φ1 and φ2 respectively, it can be shown that the ‘dark’ state (i.e. the state uncoupled from the laser fields) takes evacuated the form[25]:
 − iE2 t 2 i(ω t+φ ) 2 i(ω t+φ ) | =e h¯ e 1 1 |1− e 2 2 |3 (2) NC ˜ ˜ ˜ where E2 is the energy of the bare state |2,and = Transmission (a.u) 2 2 ·5 1 + 2.The coupled state is orthogonal to this, and

·5 therefore if the relative phase between the two lasers changes ·5 sufficiently quickly, a dark state at one instant of time will rapidly oscillate between a dark and bright state. In our − 1000 − 500 0 500 1000 ν pump (MHz) experiment it can be seen that the mutual coherence between the lasers over the timescale in which the EIT peaks are Figure 8. Probe transmission spectrum for different argon gas pressures under parallel circularly polarized fields. The top trace is recorded is sufficient for the preservation of some atomic with the cell evacuated (≈10−4 mbar) and the traces taken at coherence. This may, however, be expected to contribute to increased pressure lie below this. The bottom three traces are scaled the observed linewidth of the dark resonances. vertically by a factor of 5 and all have been shifted vertically for One significant difference between the lithium D1 and D2 ease of comparison. transitions is that the former couples ground state atoms to 2 the P1/2 levelwith well-separated hyperfine states, whilst the beam. In a dilute medium such as a gas, the absorption of this 2 latter involves the P3/2 level with different |Fe states separated beam is then given by the imaginary part of the susceptibility, by 9 MHz or less, which is less than the Rabi frequency for the whichis, in turn, proportional to the imaginary part of the allowed one-photon transitions. coherence between the bare states of the transition coupled to theprobe beam. If the probe laser corresponds to field ε1, 4.2. Resonances at the D1 transition ρ it is the reduction in the magnitude of Im[ 12]thatresults in The width of the P1 and P2 peaks can be seen to be EIT, and this can be seen from several sources in the literature significantly less than that of the other features in the spectrum. to occur when the Raman resonance condition is fulfilled; for In the collinear configuration the width of the EIT peaks recent reviews, see [23, 24]. should be determined principally by the coherence of the lasers, In this experiment, the lasers are not locked to each other, power broadening due to the pump beam, beam divergence and therefore the visibility of features that rely upon their andtransit-time broadening. The residual Doppler broadening mutual coherence can be expected to be diminished. If the (associated with the differential Doppler shift due to the incident electric fields in figure 1 are represented by cosines different wavelengths of pump and probe) is estimated to be

115 FMagnus et al ≈100 kHz, and is therefore negligible on this scale, as is the the non-coupled state and that optical pumping is needed to rate of decay of the ground state coherence. The EIT features increasethis population substantially. This may also contribute in figure 3 have a full width at half maximum which is slightly to the EIT being more pronounced for collinear beams as the less than 6 MHz, and is consistent with a spectral feature with interaction volume is much larger in the collinear beam setup. sub-natural linewidth being broadened by small amounts of Finally, we turn to an analysis of the relative heights of the inhomogeneous and homogeneous broadening. features that are due to conventional optical pumping. These For the other resonances in figure 3 the energy spread of the depend bothonthe transition dipole moments of the transitions excited states that participate intheoptical pumping process involved and on the number of subsystems that contribute to also contributes to the width (states within the 2Pmanifold the resonance. The feature height is indeed consistent with have a radiative lifetime of 27 ns). The width of these other the number of subsystems with (T) being largest, then (V) resonances (≈20 MHz) is consistent with the limiting width and (P/D) and finally (F) being the smallest. The F1–F4 (displayed by the EIT peaks) broadened due to one-photon dips are the simplest to analyse quantitatively as each is only transitions involved in the optical pumping process. due to one four-level subsystem (encompassing in general 16 The increased broadening of all resonances visible in Zeeman sublevels). Under parallel linear polarization F1 is figure 5 is principally due to theangleatwhichthebeamscross. larger than F2 and F4 is larger than F3,whilst for parallel If two laser beams with similar laboratory frame frequencies circularly polarized light F1 is larger than F2 and F3 is larger cross at a small angle of θ radians, then the Doppler width due than F4. to a gas composed of atoms travelling in all directions at speed An approximate model that can describe this behaviour v is given by is one that uses an Einstein rate equationapproach [27] to v describe the evolution of the atoms under the influence of ν = 2ν¯ θ, (3) c the pump laser.Thepump laser is assumed to excite the | where ν¯ is the mean frequency of the lasers in the laboratory population within the Zeeman sublevels of a particular Fg | frame. The average speed of lithium atoms at 700 K is about state to sublevelsoftherelevant Fe state shown in figure 4 − 1500 m s 1,soforacrossing angle of 3–4 mrad the total for the spectral features F1−4.The forms of the coupled | broadening is ≈30 MHz. The width of the central peak in differential equations fortheexcited states, e ,and ground | figure 5 is indeed seen to be about 50 MHz, which is consistent states, g ,are: with what we expect. dNe = ( − )ρ − We attribute the decrease in contrast of the optical Bge Ng Ne ANe (4) dt pumping features with increased buffer-gas pressure in figure 6  to velocity changing collisions between atoms of argon and dNg = Bge(Ne − Ng )ρ + AigNi , (5) lithium. Optical pumping relies on the laser fields interacting dt i with thesamevelocity group of atoms for long enough for where each ground state is coupled by the pump laser to the pumping to take place. Collisions with the background gas appropriate excited state by light of spectral energy density, ρ, cause the lithium atoms to change their velocity so that they and a particular excited state |i radiatively decays with total no longer see the laser fields at the same frequencies. Frequent rate A,but with partial decay rate of A to ground state |g. collisions mean that the laser fields are constantly interacting ig The absorption of the probe laser at time t after an atom enters with ‘fresh’ atoms which have not had time to be optically the laser beams, R (t),isthen assumed to be proportional pumped. abs to the sum of the population in each Zeeman sublevel times There are a number of possible reasons for the sharpening its transition dipole moment [18] to the excited state dictated of the EIT peaks when a small amount of background gas by the polarization of the probe laser. We have calculated is released into the cell. One explanation is that frequent the relative values of Rabs(t) for a pump beam spectral energy collisions between the argon and lithium atoms increase the density of 5 × 10−13 Jm3 s, which is consistent with a pump time the lithium spends in the beam thus allowing more optical beam power of 3 mW in a 2 mm diameter beam, and linewidth pumping into the non-coupled state. Pumping into the non- of 1 MHz. Figure 9 shows the calculated Rabs(t) for each coupled state will take place as long as the condition of of the four ‘F’resonances for the field polarizations shown in Raman resonance holds which, in contrast with single-photon figure 6. It can be seen that at times corresponding to those that resonance, is largely independent of the atoms’ velocity. It is an average atom is in the laser field (1–2 µs), F1 is larger than well known that collisions causing decay between the ground F2 for both polarizations whereas the relative strengths of F3 states should have a negative effect on coherent population and F4 reverse between polarizations. This is consistent with trapping but it is also well known that collisions with rare the behaviour of these resonances in figure 6, and indicates gases such as He, Ne and Ar which have no nuclear spin do that a rate equation approach is able to qualitatively explain not cause dephasing of the ground states [26]. Additionally, the effect of laser polarization onthesesubsystems. At because the argon is free to move out from the hot centre of spectral energy densities greater than that of saturation [27] the the vapour cell and cool down whereas the lithium vapour is atomic dynamics is determined principally by the spontaneous confined to the centre, the argon will be colder than the lithium. decay rate of each transition, and so these plots are relatively Elastic collisions will therefore tend to decrease the average insensitive to the precise value chosen for ρ. speed of the lithium atoms, increasing the time they spend in thebeam.The above reasoning would suggest that the small 4.3. EIT at the D2 transition P1 and P2 peaks observed with no buffer-gas present are Electromagnetically induced transparency is observed to be mostly due to the initial projection of the ground states onto less prominent on the D2 line than on the D1 line in 7Li. This

116 Optical pumping and electromagnetically induced transparency in a lithium vapour

π π π F1 resonance, π F2 resonance, F3 resonance, F4 resonance, 1 1 1 1 0.8 0.8 0.8 0.8 0.6 0.6 0.6 0.6 (t) (a.u)0.4 0.4 0.4 0.4 abs 0.2 0.2 0.2 0.2 t (µs) t (µs) t (µs) t (µs) 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 σ σ σ F1 resonance , σ F2 resonance, F3 resonance, F4 resonance, 1 1 1 1 0.8 0.8 0.8 0.8 (a.u) 0.6 0.6 0.6 0.6 (t)0.4 R 0.4 0.4 0.4 abs

R 0.2 0.2 0.2 0.2 t (µs) t (µs) t (µs) t (µs) 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

Figure 9. Relative values (with consistent scaling for each plot) of the theoretically predicted absorption of the probe laser predicted by an Einstein rate-equation approach for the four resonances labelled F1 to F4 in figure 6 under parallel linear and parallel circularly incident laser fields.

Fe=0 Fe=0 Fe=0 (a) Fe=1 (b) Fe=1 (c) Fe=1 Fe=2 Fe=2 Fe=2

Fe=3 Fe=3 Fe=3

Fg=2 Fg=2 Fg=2

Fg=1 Fg=1 Fg=1 MF -3 -2 -10 123 MF -3 -2 -10 123 MF -3 -2 -10 123

Fe=0 Fe=0 (d) Fe=1 (e) Fe=1 Fe=2 Fe=2

Fe=3 Fe=3

Fg=2 Fg=2

Fg=1 Fg=1 MF -3 -2 -10 123 MF -3 -2 -10 123

7 Figure 10. (a), (b), (c): All allowed transitions between MF states that comprise the two-beam interaction at the D2 transition in Li under (a) incident parallel linear polarization, (b) parallel circular polarization and (c) orthogonal circular polarization. Lambda transitions are denoted by bold lines, and transitions that are not part of a lambda system are denoted by light lines. (d) and (e): Transitions linking any two states with different values of Fg are shown for incident orthogonal linear polarization fields in which one of the linearly polarized field is (d) assumed to be of the higher frequency, and (e) assumed to be of lower frequency. For clarity in these last two subfigures, other transitions that are not part of a system that can coherently couple the two ground states are omitted. is in agreement with the results of Stahler¨ et al [7] who find states with the possibility of being excited on a number of greater contrast of the dark resonance on the D1 line than the non- transitions (denoted by light lines), which can reduce D2 line of rubidium. They attribute this to the closely spaced the population that is trapped. A close look at figure 10(a) hyperfine excited states of the D2 line which are not part of shows the presence of a ‘leaky’ transition from |Fg=2but any  system.Atoms can escape from the non-coupled state not from |Fg = 1.Ifthepresence of leaky- systems was through one-photon excitation to states which are not part of the principal factor that determined the behaviour of the EIT the  system, which could be termed a ‘leaky  system’. resonances at the D2 transition, then when the frequency of As the excited states are closely spaced compared to the the pump laser is scanned and the transmission of the probe incident Rabi frequencies, at Raman resonance each laser field laser is recorded, it would be expected that there would be a can excite from either the |Fg = 1 or |Fg = 2 sublevels to significant difference between the EIT features on either side all upper-state levels permitted bythe electric dipole selection of the spectrum, corresponding to whether the probe or the rules. When the pump laser is 800 MHz red-detuned with pump laser coupled with the ‘leak’ transition. This, however, respect to the probe, then the probe laser interacts with the we do not observe. Moreover, the presence or absence of a |Fg = 1↔|Fe = 0, 1, 2 transitions andthepump laser leaky- system does not explain the lack of any EIT feature mediates the |Fg = 2↔|Fe = 1, 2, 3 transitions. The at the D2 transition under parallel linearly polarized fields, as opposite is true at the high-frequency Raman resonance in the the same situations exist for both these polarizations. spectra shown above. Figure 10showstheallowed transitions The most likely explanation for the presence of EIT at between the Zeeman sublevels of the D2 line of 7 Li for a variety the D2 transition in 7Li under parallel circularly polarized of different incident polarizations. fields, and its absence under parallel linearly polarized fields, For parallel linearly and parallel circularly polarized fields can be inferred from the presence or absence of ‘double- (figures 10(a) and (b)) there are four and five possible   systems’ [28]. It is known that, in systems with closed systems, respectively (denoted by bold lines). The excited interaction contours, unless the total interaction phase, ,is state population can spontaneously decay to several ground an integer number of π,thenthere is destruction of EIT [29].

117 FMagnus et al This total phase is dependent upon the phase of the light butthese results from lithium have provided some insight fields and it can be seen from figure 10(a) that all lambda towards this goal. systems have a closed interaction contour, whilst there is a  system without a closed contour (albeit a ‘leaky’ one) in Acknowledgments figure 10(b). As we are using lasers that are not phase- locked, it is highly unlikely that the required phase relation We thank Pierre Cladefora´ ssistance with the design and for incident parallel linearly polarized fields is met [30]. It construction of the lithium vapour cell. We gratefully should be noted that experiments using phase-locked lasers acknowledge Dr B Garraway for useful discussions and the have demonstrated the presence of EIT in a system with referees for helpful comments. This work was funded by closed interaction contours [31]. Figure 10(c) corresponds EPSRC and supported by the Cold Molecules TMR Network to orthogonal circularly polarized fields; here only closed under Contract No. HPRN-CT-2002-00290. contours are present, and there was no EIT observed. We observe EIT under orthogonal linearly polarized fields, and References figures 10(d) and (e) denote the interaction systems that are [1] Lukin M D 2003 Rev. Mod. Phys. 75 457 present in this case (where one light beam is linearly polarized, [2] Harris S E 1989 Phys. Rev.Lett. 62 1033 and the other a superposition of left-hand and right-hand [3] Hau L V, Harris S E, Dutton Z and Behroozi C H 1999 Nature circular polarizations). When the linearly polarized light is at 397 594 higher frequency (i.e. figure 10(d)) and when this is the lower [4] Kash M M, Sautenkov V A, Zibrov A S, Hollberg L, frequency (i.e. figure 10(e)) there remains coherent coupling Welch G R, Lukin M D, Rostovtsev Y, Fry E S and | = | = Scully M O 1999 Phys. Rev.Lett. 82 5229 between several levels in the Fg 1 and Fg 2 levels [5] Qi J, Spano F C, Kirova T, Lazoudis A, Magnes J, Li L, with interaction contours that are not closed. These systems Narducci L M, Field R W and Lyyra A M 2002 Phys. Rev. are more complicated extensions of the three-level  system Lett. 88 173003 shown in figure 1, and some of these have been previously [6] Arimondo E, Inguscio M and Violino P 1977 Rev. Mod. Phys. studied (the four-level tripod system, for example, seen in 49 31 [7] Stahler¨ M, Wynauds R, Knappe S, Kitching J, Hollberg L, figure 10(d), can exhibit EIT without the strict phase condition Taichenachev A and Yudin V 2002 Opt. Lett. 27 1472 discussed above being satisfied [32]). [8] Nagel A, Affolderbach C, Knappe S and Wynauds R 1999 Phys. Rev. A 61 012504 5. Conclusions [9] Renzoni F, Maichen W, Windholz L and Arimondo E 1997 Phys. Rev. A 55 3710 This experiment has provided the first evidence of [10] McGloin D, Dunn M H and Fulton D J 2000 Phys. Rev. A 62 electromagnetically induced transparency at the D1 and D2 053802 transitions in 7Li atoms. The D1 line of lithium has revealed 11 [11] Badger S D, Hughes I G and Adams C S 2001 J. Phys. B: At. resonances on a Doppler background. These are due to optical Mol. Opt. Phys. 34 L749 [12] Sundholm D and Olsen J 1990 Phys. Rev. A 42 2614 pumping and saturation in different four-level subsystems of [13] Taˇıchenachev A V, Yudin V I, Wynauds R, Stahler¨ M, the D1 line and electromagnetically induced transparency. It Kitching J and Hollberg L 2003 Phys. Rev. A 67 033810 has been shown that the EIT peaks are strengthened by the [14] Weast R C 1971 Handbook of Chemistry and Physics 52nd introduction of argon buffer-gas into the lithium vapour cell. edn (Boca Raton, FL: CRC Press) This may be due to argon atoms from the colder regions of [15] Radziemski L J, Engleman R Jr and Brault J W 1995 Phys. Rev. A 52 4462 the cell reducing the velocity of the lithium atoms in the [16] Arnold A S, Wilson J S and Boshier M G 1998 Rev. Sci. interaction region, thus allowing more optical pumping into the Instrum. 69 1236 non-coupled state to take place. Velocity changing collisions [17] Windholz L 1995 Appl. Phys. B 60 573 are, however, detrimental to the optical pumping which relies [18] Zare R N 1987 Angular Momentum: Understanding Spatial on one-photon resonance with individual transitions as this Aspects in Chemistry and Physics (New York: Wiley) [19] Wong V, Boyd R W, Stroud C R Jr, Bennink R S and depends on the velocity of the atoms relative to the fields. Marino A M 2003 Phys. Rev. A 68 012502 This is not the case for optical pumping into the non-coupled [20] Blum K 1981 Density Matrix Theory and Applications (New state. The resonances in the collinear configuration are sharper York: Plenum) than in thecrossed configuration, although this latter case [21] Shore B W 1990 The Theory of Coherent Atomic Excitation does allow separation of the probe and pump beams for all (New York: Wiley) [22] Ackerhalt J R 1980 Opt. Lett. 6 136 polarization conditions. [23] Arimondo E 1996 Prog. Opt. 35 257 There are fewer resolved resonances present on the D2 [24] Marangos J P 1998 J. Mod. Phys. 45 471 line of lithium and the contrast of the dark resonance is much [25] Magnus F 2004 MSc Thesis University of Sussex diminished, and only visible for parallel circularly polarized [26] Brandt S, Nagel A, Wynauds R and Meschede D 1997 Phys. andorthogonally linearly polarized light. Consideration of Rev. A 56 R1063  [27] Loudon R 2000 TheQuantum Theory of Light 3rd edn the presenceofleaky- systems does not appear to provide (Oxford: Oxford University Press) an explanation for the observed behaviour. Instead the [28] Korsunsky E A and Kosachiov D V 1999 Phys. Rev. A 60 4996 dependence of EIT on the polarization on the D2 line of 7Li can [29] Kosachiov D V, Matisov B G and Rozhdestvensky Yu V 1992 be explained through the presence, or absence, of systems with J. Phys. B: At. Mol. Opt. Phys. 25 2473 closed interaction contours. More theoretical and experimental [30] Mazets I E, Matisov B G, Cerboneshi E and Arimondo E 1997 Phys. Lett. A 229 77 work is required to fully understand the general problem of [31] Windholz L 2001 Phys. Scr. T 95 81 the absorption of bichromatic laser light by an optically dense, [32] Paspalakis E and Knight P L 2004 J. Opt. B: Quantum gaseous sample of atoms with many internal quantum states, Semiclass. Opt. 4 S372

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