Nonadiabatic approach to quantum optical information storage A. B. Matsko, 1 Y. V. Rostovtsev, 1 O. Kocharovskaya, 1,2 A. S. Zibrov, 1,3 and M. O. Scully 1,4 1 Department of Physics and Institute of Quantum Studies, Texas A&M University, College Station, Texas77843-4242 2 Institute of Applied Physics, RAS, Nizhny Novgorod, Russia 3 P. N. Lebedev Institute of Physics, Moscow 117924, Russia 4 Max-Planck-Institut fu ¨r Quantenoptik, D-85748 Garching, Germany ~Received 17 May 2001; revised manuscript received 11 July 2001; published 17 September 2001! We show that there is no need for adiabatic passage in the storage and retrieval of information in the optically thick vapor of Lambda-type atoms. This information can be mapped into and retrieved out of long-lived atomic coherence with nearly perfect efficiency by strong writing and reading pulses with steep rising and falling edges. We elucidate similarities and differences between the ‘‘adiabatic’’ and ‘‘instant’’ light storage techniques, and conclude that for any switching time, an almost perfect information storage is possible if the group velocity of the signal pulse is much less than the speed of light in the vacuum c and the bandwidth of the signal pulse is much less then the width of the two-photon resonance. The maximum loss of the information appears in the case of instantaneous switching of the writing and reading fields compared with adiabatic switching, and is determined by the ratio of the initial group velocity of the signal pulse in the medium and speed of light in the vacuum c, which can be very small. Quantum restrictions to the storage efficiency are also discussed. DOI: 10.1103/PhysRevA.64.043809 PACS number~s!: 42.50.Gy, 03.67.2a, 42.65.Tg I. INTRODUCTION A possibility of classical storage of optical information by employing atomic coherence was recognized early on in stimulated photon-echo experiments in two-level systems @1# and multilevel media @2–4#. Storage of optical information here means that one seeks to ‘‘store’’ and ‘‘retrieve’’ an op- tical pulse on demand without distortion of the pulse shape. Usually, the photon-echo technique does not provide com- plete quantum information about a signal pulse, i.e., the re- trieved light pulse has a different shape compared with the initial shape. However, two- and three- excitation-pulse pho- ton echoes can be used @5#, but the decay time of the storage of information is determined by the transverse relaxation time, which is quite short. To increase the storage time, photon echo based on Ra- man transitions has been realized @6,7#. By using stimulated photon echo via spectrally ordered long-lived Zeeman coher- ences @2# not only has the storage time been elegantly in- creased, but also a pulse-shape storage has been achieved. Quite recently, it has been predicted that coherent atomic media are capable of demonstrating nonlinear optical effects at the few-photon level @8,10,11# and this gives an opportu- nity to store and retrieve quantum states of light @12,13#. Proof-of-principle experiments confirm this theoretical pre- diction @14–16# in the classical light limit. The basic idea of light storage via atomic coherence can be understood in terms of light interaction with L -type at- oms. Strong ‘‘writing’’and weak ‘‘signal’’light pulses propa- gate in a gas of three-level L type atoms and excite a spatial profile of a long-lived coherence between ground states u c & and u b & of the atom ~Fig. 1!. This coherence profile stores information about these pulses after they have left or have been absorbed by the medium. Subsequently, sending a strong ‘‘reading’’ pulse into the medium results in its Raman scattering off the atomic coherence and generation of a ‘‘re- trieved’’ pulse. Ideally, the retrieved pulse can be identical to the signal pulse, i.e., it possesses: ~i! the same carrying fre- quency, ~ii! the same profile and quantum statistics, and ~iii! propagates in the same direction as the signal pulse @12#. That is why the term ‘‘light storage’’ instead of the term ‘‘information storage’’ sometimes is used in the literature. Concerning the issue of how we should think about ‘‘stored light,’’ we point to a similar situation in quantum teleportation. There, we are sending information from one point in space to another and claim that by using a light beam we may, in fact, teleport an atom having one state vector to an atom some place else in space having the iden- tical state vector. One could argue that we are not teleporting atoms, we are simply teleporting information. However, all atoms are the same and so, as one argues in the teleportation game, once we have prepared any atom in a state identical to any other atom, we have indeed, teleported the atom. Now the same sort of logic could be applied to the ‘‘stopped light’’ experiments. If the ‘‘readout’’ in experiments @15,14# is, in principle, identical to the incident light and the quantum state of the light can be reproduced precisely in the spirit of the teleportation, then we might say that the light was ‘‘stored’’ in the medium and released after that. However, generally speaking, the properties of the re- trieved pulse depend on the reading pulse. For example, if the reading field pulse is centered about a frequency other than that of the the writing field, and propagates in the op- posite direction to the writing field, then the retrieved pulse propagates in the same direction as the reading field and has indeed a different frequency from the incident writing field @16#. This is impossible if the light is really stored in the medium. Therefore, the exchange of the terms ‘‘stored infor- mation’’ and ‘‘stored light’’ is not always valid. As was pointed out in Refs. @12#, the necessary condition for the retrieved pulse to resemble the signal pulse is the adiabaticity. The switching time for the reading and writing PHYSICAL REVIEW A, VOLUME 64, 043809 1050-2947/2001/64~4!/043809~11!/$20.00 ©2001 The American Physical Society 64 043809-1