OPTICAL BISTABILITY WITH RYDBERG ATOMS
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1 OPTICAL BISTABILITY WITH RYDBERG ATOMS W. Lange, W. Schulz, H. Walther, M. Pernigo, L. Lugiato To cite this version: W. Lange, W. Schulz, H. Walther, M. Pernigo, L. Lugiato. OPTICAL BISTABILITY WITH RYDBERG ATOMS. Journal de Physique Colloques, 1988, 49 (C2), pp.c281c284. < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1988 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
2 JOURNAL DE PHYSIQUE Colloque C2, Supplement au n06, Tome 49, juin 1988 OPTICAL BISTABILITY WITH RYDBERG ATOMS W. LANGE*, W. E. SCHULZ", H. WALTHER*., M. PERNIGO' ' and L. LUGIATO* ax~lanck~nstitut fiir Quantenoptik, GarchingbeiMiinchen, F.R.G. '~ektion Physik der Universita't Miinchen, GarchingbeiMiinchen, F.R.G. "'~ept. of Physics. Drexel University, Philadelphia, PA 19104, U.S.A. +Dipartimento di Fisica del Politecnico, Torino, Italy Resume On presente une experience sur la bistabilite optique d'absorption i un nombre extremement petit de photons et d'atomes. On sly sert du couplage fort entre des atomes Rb de Rydberg et le champ Blectrique i l'interieur d'une cavite supraconductrice de microondes. Cela permet d'etudier l'influence des fluctuattons sur le comportement d'un systeme bistable. Abstract We present an experiment on absorptive optical bistability at extremely low photon and atom numbers, making use of the strong coupling of Rydberg Rb atoms to the electric field in a superconducting microwave cavity. This allows to study the influence of fluctuations on the behaviour of a bistable device. 1. Introduction Research in optical bistability has been rapidly expanding since its first experimental demonstration in 1974 /1,2/. Its potential application in photonic logic has spurred the interest in the miniaturization of optical bistable elements. Fluctuations and noise in a bistable system, as an example of a nonlinear system far from thermal equilibrium, have attracted widespread interest both theoretically /3,4/ and experimentally /5,6/. Thermal fluctuations /7/ and quantum fluctuations /8,9/ scale inversely to the number of photons and atoms, respectively. A microscopic device, containing only a few atoms and photons, should represent a good system to study these effects. Bistability at low photon numbers can be achieved if Rydberg atoms are chosen as the nonlinear medium, taking advantage of their extremely strong coupling to the electromagnetic field /lo,11/. He describe a Rb atomic beam experiment to observe bistability in a microwave cavity with about ten photons. 2. Theoretical Considerations The steadystate behaviour of a bistable system is determined by the bistability parameter where g is the coup1 ing constant. In order to meet the condition for absorptive bistabi 1 ity in the meanfield limit /3/, i.e. C > 4, for a small number of atoms N, one has to increase the coupling g between atoms and field, which is proportional to the transition dipole matrix element p, while at the same time decreasing the atomic and cavity relaxation rates 7 and K, respectively. Article published online by EDP Sciences and available at
3 C282 JOURNAL DE PHYSIQUE The requirements on C( and 7 are well satisfied for Rxdberg atoms as the nonlinear medium: the scaling with the effective quantum number n is /lo/ while the transition frequency decreases with n*3 and is therefore in the microwave region. The saturation photon number is correspondingly small, and may even be of the order of 10. For a given transition the minimum number of atoms necessary for bistability only depends on IC, i.e. the quality factor Q of the cavity: N = 8.(1~/7$'n~'C > 32(1~/~$*n, for C > 4. As at microwave frequencies the main contribution to Q are ohmic losses, a superconducting resonator has to be used. The principal source of fluctuations at microwave frequencies is blackbody radiation; the number nth of thermal photons in the cavity at 4.2 K is of the same order as the saturation photon number. Our numerical calculations have shown that for intensities not too close to the switching points, the system remains stable against thermal fluctuations, so that a reasonable bistability cycle is to be expected. 3. Ex~erimental Details We selected Rubidium because it can be conveniently pumped into a Rydberg level with n around 60 by means of a threestep diode laser excitation (Fig.1). The two 780 nm lasers are frequency stabilized on the fluorescence intensity of the 5 P312 and the 6 P levels, respectively. The Rydberg atoms are detected by field ionization, and the 1250 nm laser can be stabilized on the count rate. The predominant line broadening mechanism is due to the timeofflight of the Rydberg atoms traversing the microwave cavity, resulting in a 1 inewidth of approximately 100 khz. As an appropriate microwave transition for excitation in a Kband resonator we chose which yields a maximum transition dipole moment of p = 1570 eao. We thus expect a saturation photon number of 6.3. The setup of the experiment is shown in Fig.2. After excitation into the Rydberg level the atoms traverse the resonator. The incident microwave power is swept by means of a var ble a tenuator. As the saturation intensity for the Rydberg transition is only Y/c&, the transmitted power cannot be measured. Instead, the hysteresis loop can be observed in the population inversion, which is monitored by field ionization of the atoms leaving the cavity. The resonator we are currently testing is a superconducting Niobium resonator, where the RF surface resistance sets a theoretical upper limit for Q at 5.10~. The Q factor may be lowered by varying the coupling of the microwaves into the cavity.
4 18.2GHz I 44 MHz t 1 :i ZIMHi t Dower meter Fig3 Excitation scheme 2 0 $E rubidium beam oven Fg.2 Experimental setup 4, Discussion Our experimental setup should allow to achieve bistability with atom numbers of the order of In table 1 the parameters for bistability with Rb Rydberg atoms are compared to the corresponding data for the wellstudied Na Dline. With K 7 we have selected a regime in between the good and bad cavity limit, a region where the most interesting dynamical effects are expected /4 /. By varying the Q factor of the cavity and the flux of Rydberg atoms, a wide range of parameters N and C can be accessed (Fig.3). The influence of thermal fluctuations can be studied via noise induced switching at various temperatures. At a later stage of the experiment it is planned to reduce the temperature further in order to push the number of thermal photons in the resonator below 1, so that quantum fluctuations should become observable. Acknowl ed~ement This experiment has been partly funded by the European Community under its EJOB project.
5 JOURNAL DE PHYSIQUE lo5 lo1 7 Cn, 10' 10' Z 0 c! b lo3 lo8 2 0 E 3 C P' X K g lo " 10' lo lo6 ld quality factor Q of the cavity Table 1: Comparison of bistability schemes p2 7 f area T N Na DLine 6 (eao Hz 5.10~~ Hz 7.10'~ w/cm2 4.10= cm Rb Rydberg states 310' (eao)* 105 HZ 18.10~ Hz lo13 w/cm2 0.5 cm Fig. 3 Parameter range for bistability with Rb Rydberg atoms References /1/ H.M. Gibbs, S.L. McCall, T.N.C. Venkatesan, Phys.Rev.Lett. S, 1135 (1976) /2/ H.M. Gibbs, "Optical Bistability: Controlling Light with Light", Academic Press, Or1 ando 1985 /3/ L.A. Lugiato, Theory of optical bistability, in "Progress in Opticsn Vol XXI, Amsterdam 1984 /4/ H.J. Carmichael, Theory of Quantum Fluctuations in Optical Bistability, in: "Frontiers in Quantum Optics", eds. E.R. Pike, S. Sarkar, London 1986 /5/ W. Lange, F. Mitschke, R. Deserno, J. Mlynek, Phys.Rev.A 2, 1271 (1985) /6/ F. Mitschke, R. Deserno, J. Mlynek, W. Lange, IEEE QE21, 1435 (1985) /7/ L.A. Lugiato, R.J. Horowicz, J.Opt.Soc.Am.B, 971 (1985) /8/ L.A. Lugiato, G. Broggi, A. Colombo, Noise Effects in Optical Bistability, in "Frontiers in Quantum Optics", p. 231 /9/ J.S. Satchell, S. Sarkar, Quantum Theory of Optical Bistability for Small Systems, ibid. p.204 /lo/ R.F. Stebbings, F.B. Dunnings, "Rydberg States of Atoms and Molecules", Cambridge 1983 /11/ J.A. Gallas, G. Leuchs, H. Walther, H. Figger, Advances in Atomic and Molecular Physics 20, 413 (1985)
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