Optics Communications 266 (2006) 604–608 www.elsevier.com/locate/optcom Experimental constraints of using slow-light in sodium vapor for light-drag enhanced relative rotation sensing Renu Tripathi *, G.S. Pati, M. Messall, K. Salit, M.S. Shahriar Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208, United States Received 30 December 2005; received in revised form 23 May 2006; accepted 23 May 2006 Abstract We report on experimental observation of electromagnetically induced transparency and slow-light (vg c/607) in atomic sodium vapor, as a potential medium for a recently proposed experiment on slow-light enhanced relative rotation sensing [Shahriar, et al. Phys. Rev. Lett. (submitted for publication), http://arxiv.org/abs/quant-ph/0505192.]. We have performed an interferometric measurement of the index variation associated with a two-photon resonance to estimate the dispersion characteristics of the medium that are relevant to the slow-light based rotation sensing scheme. We also show that the presence of counter-propagating pump beams in an optical Sagnac loop produces a backward optical phase conjugation beam that can generate spurious signals, which may complicate the measurement of small rotations in the slow-light enhanced gyroscope. We identify techniques for overcoming this constraint. Conclusions reached from the results presented here will pave the way for designing and carrying out an experiment that will demonstrate the slow-light induced enhancement of rotation sensing. Ó 2006 Elsevier B.V. All rights reserved. PACS: 45.40.Cc; 42.50.Àp; 42.50.Nn; 82.70.Ày; 39.20.+q; 39.90.+d Keywords: Rotation sensing; Optical gyroscope; Slow-light; Electromagnetically induced transparency; Sodium vapor; Mach–Zehnder interferometer Extreme dispersion induced by electromagnetically sensing. In this case, the rotational fringe shift is aug- induced transparency (EIT) can reduce the speed or group mented by the group index or the dispersion in the med- velocity of light by many orders of magnitude compared to ium, which, for realistic conditions, can yield many the speed of light in vacuum [1–4]. Recently, there has been orders of magnitude improvement in the sensitivity of the a significant interest in the physics and applications of gyroscope [11]. slow-light. Typical applications include schemes where a An experimental implementation of the interferometric controllably varied group velocity is used to realize optical gyroscope relies on using an EIT medium, so that the coun- delay lines, buffers, etc. [5,6], as well as techniques where ter-rotating optical fields experience resonant dispersion reversible mapping of photon pulses in atomic medium along the entire optical path. A relative motion between are used for quantum state storage [7–9]. Recent proposals the medium and interferometer is also needed [11]. This have also envisioned using slow-light to enhance the rota- gives rise to a rotational fringe shift that depends on the tional sensitivity of an interferometric optical gyroscope magnitude of the dispersion in the medium. We have con- [10,11]. Such an interferometer may use slow-light induced sidered Na atoms in a dilute vapor as an example of an dispersive drag for enhanced sensitivity in relative rotation experimental medium for this purpose. We have studied EIT in Doppler-broadened optical transitions of the D1 line in Na vapor, and experimentally measured its disper- * Corresponding author. Tel.: +1 812 841 3529; fax: +1 847 491 4455. sion characteristics that are relevant to its use in a E-mail address: [email protected] (R. Tripathi). slow-light enhanced Sagnac interferometer. In particular, 0030-4018/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2006.05.061 R. Tripathi et al. / Optics Communications 266 (2006) 604–608 605 magnitudes of the index change and the dispersion, under a Fig. 1 shows energy levels selected for a three-level K- narrow EIT resonance, have been measured by a phase type system in the D1 line of Na. A frequency-tuned cw delay obtained using a homodyne detection scheme. Precise dye laser with a narrow linewidth (<1 MHz) is used to measurements of these values help us infer the dynamic derive the optical beams. The pump beam is locked to 2 2 0 range as well as the magnitude of the sensitivity enhance- the 3 S1/2, F = 1 and 3 P1/2, F = 1 transition using satu- ment [11]. An excellent agreement is obtained while com- rated absorption. The probe laser is derived by frequency paring the magnitudes of the first-order dispersion shifting the pump beam with an acousto-optic modulator estimated from the time delay of slowed optical pulses (AOM). The frequency difference between the pump and and the slope of the dispersion curve obtained from the probe laser field is set equal to the frequency-splitting 2 interferometric measurements discussed above. While the (1.772 MHz) between the ground-states 3 S1/2, F = 1 and 2 results on slow-light in hot Na vapor have significant rele- 3 S1/2, F =2. vance to other potential applications, such as for optical The experimental arrangement is shown in Fig. 2. The data buffering or quantum memory, we have chosen here pump and the probe beams are cross-linearly polarized. to focus only on the issues that are most relevant to the They propagate collinearly in a 10 cm long sodium vapor application of this process to the enhancement of rotation cell. The beams are focused inside the cell to a beam waist sensing. (1/e in intensity) of 100 lm that corresponds to a confo- cal distance of 5 cm. The orthogonality of the pump and the probe polarizations allows us to filter the pump at the output in order to measure the absorption and dispersion 2 2 F’=1 3 P1/2 Δ 3 properties of the probe field very accurately. As the laser δ excitation in alkali atoms like sodium involves many hyper- fine Zeeman sublevels, the K-type scheme often departs from an ideal EIT system in the presence of a stray mag- ω netic field. The cell is, therefore, magnetically shielded ω 2 589.8 nm 1 using two-layers of l-metal to minimize the effects of stray Pump Probe magnetic fields. During the experiment, the sodium cell is heated to a steady temperature of 100 °C using bifilarly 2 wound coils that produce a negligible magnetic field. 2 F=2 As shown in Fig. 2, the frequency of the probe is contin- 3 S1/2 1.772 GHz 1 uously scanned around the two-photon resonance condi- F=1 tion, using a double-pass acousto-optic frequency shifter Fig. 1. Energy level structures in D1 line of sodium used as a three-level to observe the linewidth of EIT. The pump intensity is K-system. set to nearly 20 W/cm2, which corresponds to a Rabi PZT Mirror NDF Interferometer HWP BS PBS PBS Det PC Det Arb. Pulse Probe Pol Gen. HWP Lens Lens Magnetically Back-prop. shielded Na pupump vapor cell BS NDF AOM 2 Freq. Mixer AOM 1 f = 80 MHz f =1.661 GHz Pump PBS HWP Dye Laser Ar+ Laser Fig. 2. Experimental setup used to observe EIT, slow-light and PC in Na vapor. HWP = half-wave plate; PBS = polarizing beam splitter; NDF = neutral density filter; AOM = acousto-optic modulator; Pol = polarizer; and Det = detector. 606 R. Tripathi et al. / Optics Communications 266 (2006) 604–608 frequency X 40 GHz. The ratio of the pump to probe 0.1 EIT resonance intensities is set to 10. The EIT linewidth is found to be Δn 0.08 linear dispersion regime -13 -1 1 MHz. This is limited by the transit time (1 ls) of ) dn/dω ~ 1.89 x 10 Hz the atoms and can be improved upon by adding a buffer -8 0.06 gas in the vapor cell. A maximum probe transmission of 0.04 n (x 10 23% has been observed. Fig. 3a shows a sequence of EIT Δ 0.02 resonances with increasing pump intensity. A frequency- 0 dithered lock-in-detection is used to observe the EIT signal in the presence of the residual-pump beam. Fig. 3b shows -0.02 the corresponding change in the slope of the lock-in-detec- -0.04 tion signal with increasing in pump intensity. -0.06 The dispersion characteristic associated with sub-natu- Magnitude (a.u.) & -0.08 ral EIT line-widths is measured using a homodyne method [13] based on a Mach–Zehnder interferometric configura- -0.1 tion, as shown in Fig. 2. An unperturbed fraction of the -5 -4 -3 -2 -1 0 1 2 3 4 5 δ (ω -ω ) (MHz) probe beam traversing an equivalent optical path outside 2 1 the cell is used as a reference beam in the homodyne detec- Fig. 4. Interferometrically measured refractive index variation associated tion scheme. The reference beam and the transmitted EIT with EIT dispersion. signal are interferometrically combined at the output. The signal intensity detected on the photodiode is propor- tional to the phase shift D/ =(2p/k)[n(x) À 1]L, intro- Fig. 4 shows the index variation as a function of the differ- duced by the dispersion of the atomic medium, and is ence frequency d. Several measurements were taken to given by iD / 2jEpjjErefjcos[D/ + /ref], where Ep and Eref measure the slope of the positive dispersion profile at the are the amplitudes of the probe and the reference, respec- center of the EIT resonance i.e., (on/ox)jd =0 (1.89 · À13 À1 tively, L is the active interaction length, and /ref is the 10 rad s) that corresponds to a slow group velocity phase of the reference beam.