VoLUME 57, NUMBER 14 PHYSICAL REVIEW LETTERS 6 OcTosER 1986

Observation of Quantum Jumps in a Single Atom

J. C. Bergquist, Randall G. Hulet, Wayne M. Itano, and D. J. Wineland Time and Frequency Division, Jtiational Bureau ofStandards, Boulder, Colorado 80303 (Received 23 June 1986)

%e detect the radiatively driven electric quadrupole transition to the metastable Dsy2 state in a single, laser-cooled Hg D ion by monitoring the abrupt cessation of the fluorescence signal from the laser-excited 'Si/2 Pi~2 first resonance line. %hen the ion "jumps" back from the metastable D state to the ground S state, the S P resonance fluorescence signal immediately returns. The sta- tistical properties of the quantum jumps are investigated; for example, photon antibunching in the emission from the D state is observed ~ith 100% efficiency.

PACS numbers: 32.80,Pj, 42.SO.Dv

Recently, a few laboratories have trapped and radia- ground state to the 5d 6s D5/2 state near 281.5 nm. tively cooled single atoms' 4 enabling a number of The lifetime of the metastable D state has recently unique experiments to be performed. One of the ex- been measured to be about 0.1 s.'5'6 A laser tuned periments now possible is to observe the "quantum just below resonance on the highly allowed S.P transi- jumps" to and from a metastable state in a single atom tion will cool the ion and, in our case, scatter up to by monitoring of the resonance fluorescence of a 5&&10~ photons/s. By collecting even a small fraction strong transition in which at least one of the states is of the scattered photons, we can easily monitor the coupled to the metastable state. When the atomic quantum state of the atom. If only the strong transi- electron moves to the metastable state, the fluores- tion is radiatively driven, then for averaging times long cence from the strongly driven transition disappears. compared to the Pi/2 state lifetime and mean S P When the electron drops back into the strongly driven excitation time, a steady fluorescence level is expeced, transition, the fluorescence abruptly returns. Thus the corresponding to the atom rapidly cycling between the strong transition fluorescence is a monitor of the Sand P state. If radiation to drive the weak transition quantum state of the atom. Several years ago, is also admitted, then the atom will occasionally be Dehmelt had proposed this optical double-resonance driven into the metastable state and the fluorescence scheme (terming it electron shelving) as an amplifica- from the strong transition will abruptly disappear. The tion mechanism to detect a weak transition in single- cessation of the scattering of many photons on the atom spectroscopy. 5 This technique has been used for strong transition for one photon absorbed on the weak several years in high-resolution spectroscopic studies transition permits unit detection efficiency of the tran- of samples of many laser-cooled ions, achieving quan- sition to the metastable state. 6' Some time later, the tum amplifications of 10 and higher. In 1981, elec- atom returns spontaneously or is driven out of the D tron-shelving amplification was used to perform state back to the ground state, which causes a sudden optical-optical double resonance in a single, laser- return of the fluorescence on the strong transition. cooled, trapped ion. While the signal-to-noise ratio in The random on/off "telegraphic" signal provides a di- that experiment was not sufficient to see quantum rect indication of the quantum state of the ion. jumps directly, the fact that the atomic fluorescence The experimental setup is largely the same as that would be bistable was noted. More recently, the statis- tics of quantum switching in a single atom have been 2 theoretically treated in some detail first by Cook and p s '3 3/2 Kimble7 1O and subsequently by several other authors. 5d 6p In this Letter we report the clear experimental demon- 2 stration of quantum jumps in a single laser-cooled 1/2 2 '9sHg+ ion stored in a miniature radio-frequency trap. 6s The basic idea for quantum switching and the associ- ated statistics is illustrated with the three-level system shown in Fig. 1 for the Hgu ion. In Hgtt there is a "strong" resonance transition from the 5d'o6s2Si/2 ground state to the 51' 6p Pi/2 state near 194 nm. The lifetime of the 2Pi/2 state has been measured else- where to be 2.3+0.3 ns. '4 Additionally, there is a 51 6S S1/2 "weak" electric quadrupole transition from the 2Si/2 FIG. 1. Simplified optical energy-level diagram for Hg u.

Work of the U. S. Government Not subject to U. S. copyright 1699 VOLUME 57, NUMBER 14 PHYSICAL REVIEW LETTERS 6 OcToaER 1986 used in the two-photon spectroscopic study of the 70 earlier. ' In the S,/2 D5/2 transition in HgII reported present experiment, one ion (on some occasions, two »»»!I»»AI»!II»I»~I»»»»»»»»I»»»I»)»»»"»»»»I!I!6I» . below 25 ions) was loaded into the trap and cooled to E mK by 2—5»M, W of sum-frequency-generated radiation o~ near 194 nm (spot size wo -—10 p, m) tuned just below (8 the Si/2- Pi/2 first resonance transition. The fluores- &r'I»»„%'" I cence light scattered by the ions was detected at right «„II, , »», angles to the 194-nm beam with an overall detection efficiency of about 5X10 4. Peak signal counts ex- v ~' U ig 104/s a background counting rate of ceeded 2& against o t 200/s. This high counting rate permitted us to moni- 10-ms rate with a tor the fluorescence at a sampling :»~ »»le '! JI reasonable signal-to-noise ratio. The fast sampling II rate is necessary because of the 100-ms lifetime of the 0 0 2 3 D5/2 state. Radiation from a frequency-stabilized ring dye laser Time (s)— near'5 563 nm was doubled to 281.5 nm in order to FIG. 2. Samples of the quantum-jump data. (a) The drive the Si/2- D5/2 electric-quadrupole-allowed tran- fluorescence counts detected with no resonance radiation '8 sition directly. The power of the 281.5-nm radiation exciting the weak 5~~2-D5~2 transition. The few jumps ob- could be adjusted to as much as 20 p, W. The beam served are likely due to collisions with background Hg atoms was focused at the center of the trap to a spot size wo and radiative decay to the Dy2 state. (b) Both the 194- and of approximately 25 p, m. A magnetic field of approxi- 281.5-nm radiation are applied simultaneously. Compared mately 1 mT (10 G) was applied parallel to the electric to (a), the interruptions to the fluorescence signal are more field vector of the 281.5-nm radiation and perpendicu- frequent. (c) Two ions are trapped and cooled. The inter- ruptions to the fluorescence signal show two levels corre- lar to its direction of propagation. The selection rule sponding to loss of fluorescence from one or both ions. The for the electric-quadrupole-allowed transitions to the sampling rate for all the data is 10 ms per point; the length is various Zeeman states for this configuration of each sample is 4 s. 5 mJ = 1. The frequency of the 281.5-nm radiation was tuned to resonance with the 'Si/2 D5/2 (mJ ' mq = + —, ) Zeeman component for the necessary to examine the off-diagonal terms of the results here. density matrix in order to include possible coherence quantum switching reported Also, the s'3 resonance signal obtained from the Pi/2 fluorescence effects. However, for the conditions of our experi- counts during scanning of the 281.5-nm laser over this ment, that is, for times longer than the inverse of the component revealed a linewidth of less than 8 MHz. If excitation and spontaneous emission rates on the this width is due to Doppler broadening, the ion tem- strong transition, and when the excitation and emis- perature (in the pseudopotential well) is less than 25 sion rates on the strong transition exceed those on the mK and the ion is estimated to be confined to a weak transition, the dynamics of the quantum-jump volume characterized by a linear dimension of less process can be described by effective two-state rate a than 0.25»Mm. equations for coherent or incoherent excitation. As a In order to observe the quantum jumps, we monitor consequence there exist simple probabilities per unit the strong fluorescence at 194 nm while simultaneous- time R+ and R that the electron makes an upward ly admitting the 281.5-nm radiation. A computer or downward jump on the weak transition. Using the strobes and displays the detected 194-nm fluorescence theory of Ref. 8 adapted to arbitrary detuning, and counts accumulated in a counter at 10-ms intervals for with the additional condition relevant to our experi- running times of 40 s. These data are then stored and ment that the radiation driving the strong transition is the process repeated, but now without the 281.5-nm well below saturation, we find that the Einstein A coef- radiation, or, in some cases, with the 281.5-nm laser ficient for the spontaneous decay of the weak transi- detuned from resonance. We repeat the entire se- tion is related to these probabilities by quence numerous times for different po~er levels of the 281.5-nm light and for different detunings of the ~ ('D„,) = R —R+. 194-nm radiation. An example of 4 s of a sequential set of data with the 281.5-nm radiation (0.3 p, W) first From data similar to those of Fig. 2(b), we plotted the off and then on is shown in Figs. 2(a) and 2(b), distribution of off times r,rr and the distribution of on respectively. times 7,„. Theory predicts that the probability den- For the general case of coherent excitation, it is sity for the time duration of the off (and on) intervals

1700 VoLUME 57, NUMBER 14 PHYSICAL REVIEW LETTERS 6 OcToBEa 1986 is given by

fV,rr(r, rr) = R exp( —R r,rr) for time off, and by W.„(r.„)= R, exp( —R..„) (3) . CQ for time on. Thus, R+ and R are found from ex- 1150 0.5 ponential least-squares fits to the data, and from these C3 and Eq. (1) we determine the A coefficient for the me- tastable 2D2ts state. Unfortunately, the data analysis is 0.0 0.01 0,1 1,0 complicated by the background events as indicated in T Fig. 2(a). Although we have not unambiguously (s) determined their origin, two contributions are col- FIG. 3. Plots of the 194-nm floorescence intensity corre- lisions with background mercury atoms which tem- lation function C(r) and the 281.5-nm emission correlation ions2 perorarily heat the and radiative decay from the function gii(r ). Photon antibunching in the 281.5-nm emis- P&~2 state to the D3t2 state. The lifetime of the D3 sion is inferred from the observation that gD(r) 0 as state has recently been measured to be about 20 ms. 6 7~0 According to theory'9 it decays with nearly equal prob- ability to the lower-lying D5t2 state and to the ground state. We estimate'7 the probability that a mercury ion where in the 'P, state will to the state as ~2 decay 'D3tz = 3x 10 7. In the present experiment there is no direct (I) loR-/(R +R —). measure of the background pressure at the trap, but (I2) —(l)2= lo2R+ R + R--)2. estimates based on ion-pump current are consistent l(R+ with the observed frequency of background events. In Fig. 3 we plot the two-time intensity-correlation Estimated recooling rates are also consistent with the function for a typical run. The values of R+ and R data. obtained from a least-squares fit agree with those If the background interruptions in the fluorescence derived from the distributions of off and on times. signal were due solely to collisions, one would expect Other statistical properties can be derived from the their rate of occurrence to be independent of the 194- quantum switching data. For example, if one neglects nm scattering rate. The average duration of the off the background interruptions to the fluorescence sig- times after a collision would be a function of the 194- nal, each upward (downward) transition in the fluores- nm intensity and detuning, since these parameters cence can be assumed to mark the emission (absorp- in- would affect the recooling rate. If the background tion) of a D5t2-2Sit2 photon. Let gD(7) denote the terruptions were due solely to radiative decay, one probability that the (assumed) emission of a 281.5-nm would expect their rate of occurrence to be proportion- photon is followed by the (assumed) emission of al to the 194-nm scattering rate, but their average another 281.5-nm photon at a time r later, normalized duration to be fixed, since this would depend only on to 1 at r = ~. For our experimental conditions„ theory data indicate the metastable decay rates. The present predicts that gD(r) = 1 —exp[ —(R+ + R ) 7 ], and that both processes may be present in that both the this is in agreement with the data. In Fig. 3 we plot rate and the average duration of off times vary with gD(r) from some of our quantum switching data. The scattering rate. Even with these background events, fact that gD(r ) - 0 at r =0 implies the existence of we find the lifetime for spontaneous emission from photon antibunching"'3 in the 281.5-nm radiation level the 2D5t2 given by Eq. (1) to be 90+30 ms, from the Dstz state. Because of the quantum amplifi- which is in agreement with the earlier measure- cation in the S-P scattering loop the photon antibunch- ments. "" ing is detected with nearly 100'/o efficiency. Also of interest is the two-time intensity-correlation Finally, in Fig. 2(c) we show quantum switching for function' "for the 194-nm fluorescence: the case of two laser-cooled and trapped ions (estimat- = ed separation = 2.5 p, m). There are three distinct lev- &(r) (l(t)l(t+T)). (4) els of fluorescence corresponding to (a) a maximum when both ions are in the S-P scattering loop, (b) an This expression can be written as intermediate level when one ion is shelved in the D state and one ion is scattering, and (c) no fluores- C(r) = (l)'+ ((l') —(l)')exp[ —(R, + R )r], only cence in the rare cases when both ions are shelved in the D state. VoLUME 57, NUMBER 14 PHYSICAL REVIEW LETTERS 6 OcTosE~ 1986

In summary, we have demonstrated quantum jumps J. Phys. (Paris), Colloq. 42, C8-299 (1981). or switching in a single atom. We have analyzed the 6D. J. %ineland, J. C. Bergquist, %. M. Itano, and R. E. statistics and found agreement with earlier published Drullinger, Opt. Lett. 5, 245 (1980); D. J. Wlneland, W. M.

values for the lifetime of the Sd 6s 2Dsi2 state in Itano, J. C. Bergquist, J ~ J. Bollinger, and J. D. Prestage, in HgII. It is interesting to speculate about a single atom Atomic Physics, edited by R. S. Van Dyck, Jr., and E. N. in which the upper state on the weak transition is ex- Fortson (World Scientific, Singapore, 1985), Vol. 9. 7R. J. Cook and H. J. Kimble, Rev. tremely long lived and excited by adiabatic rapid pas- Phys. Lett. 54, 1023 (1985). sage. 2o In this case the random nature of the excita- H. J. Kimble, R. J. Cook, and A. L. Wells, Phys. Rev. A could realize a single-atom tion is eliminated and one 34, 3190 (1986). switch or flip flop. 9T. Erber and S. Putterman, Nature 318, 41 (1985). The authors are pleased to acknowledge the expert toJ. Javanainen, Phys, Rev. A 33, 2121 (1986). technical assistance of C. Manney during parts of this ' A. Schenzle, R. G. DeVoe, and R. G. Brewer, Phys. Rev. experiment, and the help of D. J. Larson in the earlier A 33, 2127 (1986). work to obtain single-ion cooling. We are appreciative ~2C. Cohen-Tannoudji and J. Dalibard, Europhys. Lett. 1, to H. J. Kimble for helpful discussions of "quantum 441 (1986). jumps" and to J. J. Bollinger, R. E. Drullinger, and '3D. T. Pegg, R. Loudon, and P. L. Knight, Phys. Rev. A L. Hollberg for comments on the manuscript. We 33, 4085 (1986). i4P. gratefully acknowledge the support of the U.S. Air Eriksen and O. Poulsen, J. Quant. Spectrosc. Radiat. Transfer 23, 599 (1980). Force Office of Scientific Research and the U.S. Office &5J. C. Bergquist, D. J. %ineland, %'. M. Itano, H. Hern- of Naval Research. We note that a Letter by Nagour- mati, H.-U. Daniel, and G. Leuchs, Phys. Rev. Lett. SS, ney, Sandberg, and Dehmelt2' describing quantum 1567 (1985). Ba+ jumps in a single atom has appeared subsequent i6C. E. Johnson, Bull. Am. Phys. Soc. 31, 957 (1986). to the submission of our Letter. 7D. J. Wineland, W. M. Itano, J. C. Bergquist, and F. L. Walls, in Proceedings of the 35th Annual Symposium on Fre quency Control, Phiiadeiphia, J 981 (Electronic Industries As- sociation, Washington, DC, 1981), p. 602. Neuhauser, M. Hohenstatt, P. Toschek, and &8D. J. Wineland, J. C. Bergquist, R. E. Drullinger, H. Dehmelt, Phys. Rev. A 22, 1137 (1980). H. Hemmati, W. M. Itano, and F. L. Walls, J. Phys. (Paris), 2D, J. %ineland and W. M. Itano, Phys. Lett. 82A, 75 Colloq. 42, C8-307 (1981). (1981). 9R. H. Garstang, J. Res. Natl. Bur. Stand. Sect. A 68, 61 3%. Nagourney, G. Janik, and H. Dehmelt, Proc. Natl. (1964). Acad. Sci. U.S.A. $0, 643 (1983). 2OSee, for example, A. Abragam, Principles of Nuclear 4G. Janik, %. Nagourney, and H. Dehmelt, J. Opt. Soc. Magnetism (Clarendon, Oxford, 1961), p. 65. Am. B 2, 1251 (1985). 2~%. Nagourney, J. Sandberg, and H. Dehmelt, Phys. Rev. sH. G. Dehmelt, Bull. Am. Phys. Soc. 20, 60 (1975), and Lett. 56, 2727 (1986).