OPTICAL BISTABILITY WITH RYDBERG ATOMS

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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.C2-81-C2-84.

�10.1051/jphyscol:1988217�. �jpa-00227634�

JOURNAL DE PHYSIQUE

Colloque C2, Supplement au n06, Tome 49, juin 1988

OPTICAL BISTABILITY WITH RYDBERG ATOMS

W. LANGE* , W. E. SCHULZ" , H. WALTHER*

.

L. LUGIATO*

ax-~lanck-~nstitut fiir Quantenoptik, 0-8046 Garching-bei-Miinchen, F.R.G.

' ~ e k t i o n Physik der Universita't Miinchen, 0-8046 Garching-bei-Miinchen, 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 micro-ondes. 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 steady-state 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 mean-field 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

,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988217

C2-82 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 o f 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 satu- ration 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 three-step 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 time-of-flight 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 K-band resonator we chose

which yields a maximum transition dipole moment of p = 1570 eao. We thus expect a satu- ration photon number of 6.3.

The set-up 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.

I

4 4 MHz

t

18.2GHz

:i

1 t

Fig3 Excitation scheme

Dower meter

$E 2 - 0

oven

Fg.2 Experimental set-up

4,

Our experimental s e t - u p should a l l o w t o achieve b i s t a b i l i t y w i t h atom numbers o f t h e o r d e r o f 1000. I n t a b l e 1 t h e parameters f o r b i s t a b i l i t y w i t h Rb Rydberg atoms a r e compared t o t h e c o r r e s p o n d i n g d a t a f o r t h e w e l l - s t u d i e d Na D - l i n e .

W i t h K

-

The i n f l u e n c e o f thermal f l u c t u a t i o n s can be s t u d i e d v i a n o i s e induced s w i t c h i n g a t v a r i o u s temperatures. A t a l a t e r stage o f t h e experiment i t i s planned t o reduce t h e tem- p e r a t u r e f u r t h e r i n o r d e r t o push t h e number of thermal photons i n t h e r e s o n a t o r below 1,

so t h a t quantum f l u c t u a t i o n s s h o u l d become observable.

Acknowl e d ~ e m e n t

T h i s experiment has been p a r t l y funded by t h e European Community under i t s EJOB p r o j e c t .

JOURNAL DE PHYSIQUE

lo5 lo1°

7

Cn, Table 1: Comparison o f b i s t a b i l i t y schemes

10' 10'

2

+ 0

Z ⁰

b lo3

P'

c! lo8

2

E ^-0

3 X

C K

g

-

_-

"-

10' lo6

103 104 105 lo6 l d

quality factor

Q

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, " O p t i c a l B i s t a b i l i t y : C o n t r o l l i n g L i g h t w i t h L i g h t " , Academic Press, Or1 ando 1985

/3/ L.A. Lugiato, Theory o f o p t i c a l b i s t a b i l i t y , i n "Progress i n O p t i c s n Vol X X I , Amsterdam 1984

/4/ H.J. Carmichael, Theory o f Quantum F l u c t u a t i o n s i n O p t i c a l B i s t a b i l i t y , i n : " F r o n t i e r s i n 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 QE-21, 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 E f f e c t s i n O p t i c a l B i s t a b i l i t y , i n " F r o n t i e r s i n Quantum Optics", p . 231

/9/ J.S. S a t c h e l l , S. Sarkar, Quantum Theory o f O p t i c a l B i s t a b i l i t y f o r Small Systems, i b i d . p.204

/lo/ R.F. Stebbings, F.B. Dunnings, "Rydberg States o f Atoms and Molecules", Cambridge 1983

/11/ J.A. Gallas, G. Leuchs, H. Walther, H. Figger, Advances i n Atomic and Molecular Physics 20, 413 (1985)

Rb Rydberg states

-

3-10' (eao)*

105 HZ

18.10~ Hz lo-13 w/cm2

0.5 cm2 10-4 103 p2

7 f

area T

-

Na D-Line

6 (eao12 6.107 Hz 5 . 1 0 ~ ~ Hz 7 . 1 0 ' ~ w/cm2 4.10-= cm2

10-2 105