12. M. Greiner, C. A. Regal, J. T. Stewart, D. S. Jin, Phys. Rev. Lett. 94, 110401 (2005). 13. M. Henny et al., Science 284, 296 (1999). 14. W. D. Oliver, J. Kim, R. C. Liu, Y. Yamamoto, Science 284, 299 (1999). 15. H. Kiesel, A. Renz, F. Hasselbach, Nature 418, 392 (2002). 16. Y. Kagan, B. V. Svistunov, G. V. Shlyapnikov, Sov. Phys. JETP 42, 209 (1985). 17. E. A. Burt et al., Phys. Rev. Lett. 79, 337 (1997). 18. B. Laburthe Tolra et al., Phys. Rev. Lett. 92, 190401 (2004). 19. A. Robert et al., Science 292, 461 (2001); published online 22 March 2001 (10.1126/science.1060622). 20. O. Jagutzki et al., Nucl. Instrum. Methods Phys. Res. A 477, 244 (2004). 21. See supporting online materials on Science Online for details. 22. M. Naraschewski, R. Glauber, Phys. Rev. A 59, 4595 (1999). 23. L. Deng et al., Nature 398, 218 (1999). 24. J. Vogels, K. Xu, W. Ketterle, Phys. Rev. Lett. 89, 020401 (2002). 25. R. Stas, J. McNamara, W. Hogervorst, W. Vassen, Phys. Rev. Lett. 93, 053001 (2004). 26. A. O ¨ ttl, S. Ritter, M. Ko ¨hl, T. Esslinger, Phys. Rev. Lett. 95, 090404 (2005). 27. After submission of this manuscript, we became aware of a related experiment concerning atom correla- tions in an atom laser (26). We thank R. Sellem of the De ´tection Temps, Position Image Technology Division (supported by the Mission Ressources et Compe ´tences Technologiques–CNRS Federation FR2764 and by the Universite ´ Paris-Sud) for a decisive role in the develop- ment of the time-to-digital converter, and O. Jagutzki for advice on delay lines. Supporting Online Material www.sciencemag.org/cgi/content/full/1118024/DC1 SOM Text 27 July 2005; accepted 5 September 2005 Published online 15 September 2005; 10.1126/science.1118024 Include this information when citing this paper. Quantum Coherence in an Optical Modulator S. G. Carter, 1 * V. Birkedal, 1 . C. S. Wang, 2 L. A. Coldren, 2 A. V. Maslov, 3 D. S. Citrin, 4,5 M. S. Sherwin 1 - Semiconductor quantum well electroabsorption modulators are widely used to modulate near-infrared (NIR) radiation at frequencies below 0.1 terahertz (THz). Here, the NIR absorption of undoped quantum wells was modulated by strong electric fields with frequencies between 1.5 and 3.9 THz. The THz field coupled two excited states (excitons) of the quantum wells, as manifested by a new THz frequency- and power-dependent NIR absorption line. Nonpertur- bative theory and experiment indicate that the THz field generated a coherent quantum superposition of an absorbing and a nonabsorbing exciton. This quan- tum coherence may yield new applications for quantum well modulators in optical communications. Quantum three-state systems in which two of the states are strongly coupled by an intense laser field have been widely studied in atom- ic and molecular systems (1). The energies of the quantum states are altered as they are Bdressed[ by the strong light-matter interac- tion. Such dressed states were first observed by Autler and Townes (AT) in a molecular system driven by a strong radio-frequency field and probed by weak microwaves (2). When a radio-frequency resonance occurred, the micro- wave absorption line split in two. In three-state systems with weak coupling to the environ- ment, AT splitting can evolve into electromag- netically induced transparency (EIT), in which a strong coupling beam induces transparency at a resonance at which the undriven system is opaque (3). This transparency is due to quan- tum interference between the dressed states. EIT is the basis for slow (4) and stopped light (5, 6) in atomic systems. A variety of quantum systems similar to atomic three-state systems can be engineered in semiconductor quantum wells (QWs). A QW is a layer of one semiconductor grown between semiconductors with larger band gaps (7). The layer with the smaller gap is suffi- ciently thin that well-defined sets of quantized states, or subbands, are associated with elec- tron motion parallel to the growth direction. Within each subband, there is a continuum of states associated with different momenta par- allel to the plane of the QW (perpendicular to the growth direction). AT-like splitting (8), quantum interference (9, 10), and EIT (11, 12) have been reported in QWs, but their observa- tion has been more difficult than in atoms and molecules. This is in part because of much larger absorption linewidths, which result from disorder, from stronger coupling to the envi- ronment, or from scattering between subbands. We have fabricated a particularly simple three-level system in undoped QWs (Fig. 1). The excitation with the lowest frequency oc- curs at about 350 THz (wavelength 857 nm or energy 1.46 eV) when an electron is promoted from the filled valence subband of highest energy (labeled h1) to the empty conduction subband of lowest energy (labeled e1). The excited electron binds with the hole it left be- hind to form an exciton with a hydrogen-like wave function in the QW plane. Transitions between different in-plane states (e.g., the 1s and 2p states) are allowed only for in-plane THz polarizations (13, 14), which are not present in the experiments discussed here. The lowest exciton state is labeled h1X. The next exciton state, h2X, consists of an electron from e1 and a hole from the second highest valence subband, h2. NIR transitions between the crys- tal ground state and h2X are not allowed be- cause of quantum mechanical selection rules. However, intersubband transitions from h1X to h2X are allowed for THz radiation polarized in the growth direction. The three states anal- ogous to those in an AT picture are the crystal ground state, the lowest exciton h1X, and the second exciton h2X (15). This report explores the NIR absorption of undoped QWs at low temperatures (È10 K) when they are driven by strong electric fields polarized in the growth direction with frequen- cies between 1.5 and 3.9 THz. Because the frequency of the THz laser is about 1% of that required to create an exciton, the strong laser field does not alter the populations of the quan- tum states of the system. Near 3.4 THz, the drive frequency is resonant with the transition between the two lowest exciton states. The AT splitting of excitons driven by strong intersub- band radiation is experimentally observed, and theoretical predictions (16, 17) are confirmed. The sample consists of 10 In 0.06 Ga 0.94 As QWs (each 143 )) separated by Al 0.3 Ga 0.7 As barriers (300 )). InGaAs QWs were used instead of GaAs QWs so that the GaAs sub- strate was transparent for NIR light near the exciton energies. A 100-nm layer of aluminum was deposited on the surface of the sample on which the QWs were grown. The metallic boundary condition improved THz coupling and ensured that the THz field at the QWs was polarized almost perfectly in the growth direction (18). The interband absorption was probed using broadband, incoherent, NIR light from an 850-nm light-emitting diode focused onto the sample backside to a spot size È250 mm in diameter. The NIR intensity was less than 0.3 W/cm 2 . As illustrated in Fig. 1, the NIR beam was transmitted through the trans- parent substrate, interacted with the QWs, was reflected off of the Al layer, and was then collected and sent to a monochromator with an intensified charge-coupled device detec- tor. The reflected NIR beam was measured during the 1 to 1.5 ms at the peak of the THz 1 Physics Department and Institute for Quantum and Complex Dynamics (iQCD), Broida Hall Building 572, Room 3410, 2 Electrical and Computer Engineering Department, University of California, Santa Barbara, CA 93106, USA. 3 Center for Nanotechnology, NASA Ames Research Center, MS 229-1, Moffett Field, CA 94035, USA. 4 Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. 5 Georgia Tech Lorraine, Metz Technopole, 2-3 rue Marconi, 57070 Metz, France. *Present address: JILA, University of Colorado, 440 UCB, Boulder, CO 80309, USA. .ne ´e Ciulin. Present address: Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 A ˚ rhus C, Denmark. -To whom correspondence should be addressed. E-mail: sherwin@physics.ucsb.edu R EPORTS www.sciencemag.org SCIENCE VOL 310 28 OCTOBER 2005 651