VOLUME86, NUMBER 16 PHYSICAL REVIEW LETTERS 16APRIL2001Generation of Photon Number States on Demand via Cavity Quantum ElectrodynamicsSimon Brattke,1,2Benjamin T. H. Varcoe,1and Herbert Walther1,21Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany2Sektion Physik der Universität München, 85748 Garching, Germany(Received 18 August 2000)Many applications in quantum information or quantum computing require radiation with a fixed num-ber of photons. This increased the demand for systems able to produce such fields. We discuss theproduction of photon fields with a fixed photon number on demand. The first experimental demonstra-tion of the device is described. This setup is based on a cavity quantum electrodynamics scheme usingthe strong coupling between excited atoms and a single-mode cavity field.DOI: 10.1103/PhysRevLett.86.3534 PACS numbers: 42.50.Dv, 03.67.–aIn recent years there has been increasing interest insystems capable of generating photon fields containing apreset number of photons. This has chiefly arisen fromapplications for which single photons are a necessary re-quirement, such as secure quantum communication [1 –3]and quantum cryptography [4]. Fock states are also use-ful for generating multiple atom entanglements in systemssuch as the micromaser. The generated field and the pump-ing atoms are in an entangled state, this entanglement canbe transferred by the field to subsequent atoms, leading toapplications such as basic quantum logic gates [5]. In thecurrent experiment the micromaser employed a cavity witha Q value of 4 3 1010corresponding to a photon lifetimeof 0.3 s which is the largest ever achieved in this type ofexperiment and more than 2 orders of magnitude greaterthan in related setups [5]. In this cavity, Fock states can beused to entangle a large number of subsequent atoms. Asource of single photons or, more generally, arbitrary Fockstates is also a useful tool for further fundamental inves-tigations of the atom-field interaction. It can be used toobtain the reconstruction of purely quantum states of theradiation field as represented by the Fock states [6].Many sources for single photons have been proposed.These include single-atom fluorescence [7], single-molecule fluorescence [8], two-photon down-conversion[9] and Coulomb blockade of electrons [10], state re-duction [11], and using cavity quantum electrodynamics[3,12–14]. On the other hand, only one source presentedrecently, involving the transfer of atoms between amagneto-optical trap and dipole trap [15], is, in principle,able to produce n atoms. However, a reliable and deter-ministic source of Fock states (or even single photons)has not yet been demonstrated.Using the one-atom maser or micromaser we present thefirst experimental evidence for the operation of a reliableand robust source of photon Fock states, which by virtue ofits operation also produces a predefined number of atomsin a particular state. These atoms are entangled with thegenerated field and, as mentioned above, can be furtherentangled with subsequent atoms.A basic requirement for reliably preparing a field in apre-set quantum state is the ability to choose the field statein a controllable manner. Trapping states provide this con-trol. Under trapping-state conditions a quantum feedbackbetween the atoms and the field acts to control the cav-ity photon number. Using trapping states, one is thereforeable to provide photons on demand. This provides the ad-ditional benefit of eliminating the need to detect the atomsleaving the cavity, thus making these atoms available as asource for further experiments. The method we describehere is, in principle, also applicable to optical cavities [16]and is therefore of broad use.Under ideal conditions the micromaser field in a trap-ping state is a Fock state; however, when the micromaseris operated in a continuous wave (cw) mode, the field stateis very fragile and highly sensitive to external influencesand experimental parameters [17,18]. However, contraryto cw operation, under pulsed operation the trapping statesare more stable and more practical, and usable over a muchbroader parameter range than for cw operation.The cw operation of the micromaser has been studiedextensively both theoretically [19] and experimentally. Ithas been used to demonstrate quantum phenomena suchas, for example, sub-Poissonian statistics [20], the collapseand revival of Rabi oscillations [21], and entanglementbetween the atoms and cavity field [22].The micromaser setup used for the experiments hasbeen described previously [17]. Briefly, a beam of85Rbatoms is excited to the 63P3兾2Rydberg level by single-step laser excitation 共l 苷 297 nm兲. The excited atoms en-ter a high-Q superconducting microwave cavity housed ina3He-4He dilution refrigerator which cools the cavity to300 mK, corresponding to a thermal photon number nth苷0.03. The cavity is tuned to a 21.456 GHz transition fromthe 63P3兾2upper state to the 61D5兾2lower state of themaser transition.The emission probability, Pg,ofa63P3兾2upper levelatom entering the cavity is given byPg苷 sin2共pn 1 1 gtint兲 , (1)3534 0031-9007兾01兾86(16)兾3534(4)$15.00 © 2001 The American Physical SocietyVOLUME86, NUMBER 16 PHYSICAL REVIEW LETTERS 16APRIL2001where n is the number of photons in the cavity, g is theeffective atom-field coupling constant 共艐41 kHz兲, and tintis the interaction time. We note that Pg苷 0 whenpn 1 1 gtint苷 kp , (2)where k is an integer number of Rabi cycles. This is thetrapping-state condition. When it is fulfilled, the emis-sion probability is zero and the field has reached an up-per bound, thus preventing atoms from emitting. Trappingstates are denoted by the number of photons n and aninteger number of Rabi cycles k for which the emissionprobability is zero, they are labeled 共n, k兲 [18]. It is thismechanism that controls the emission probability of atomsentering the cavity when the interaction time is tuned toa trapping state where the Fock state is produced and sta-bilized by the trapping condition. For short pulse lengthsthe lower-state atom number will be the same as the pho-ton number. For simplicity we will concentrate here onthe preparation of a one-photon Fock state although themethod can also be used to generate Fock states with higherphoton numbers.For useful comparisons between experiment and theory,Monte Carlo simulations [23] are used to calculate the rateof production of lower-state atoms rather than the