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Precise Test of Quantum Jump Theory PHYSICAL REVIE% A VOLUME 37, NUMBER 11 JUNE 1988 Precise test of quantum jump theory Randall G. Hulet, D. J. Wineland, J. C. Bergquist, and Wayne M. Itano Time and Frequency Diuision, National Bureau of Standards, Boulder, Colorado 80303 (Rece]ved 16 November 1987) Quantum jumps due solely to spontaneous Raman scattering between the Zeeman sublevels of a single Mg+ ion have been observed in the fluorescence emitted by the ion. A theory of quan- tum jumps for this system predicts that coherences between excited levels cause the ratio of the mean duration of the "fluorescence-on periods" to the mean duration of the "fluorescence-off periods" to be independent of laser intensity. The measured value agrees with the predicted one to within the measurement precision of 2%. The distribution of the durations of the oA periods also agrees with theory. A few groups have recently observed "quantum jumps" and an excited P3/2 state (for example, an alkali atom or ionized alkaline earth atom). The ta of between the energy levels of a single atomic ion as sig- singly frequency— naled by an abrupt change in the fluorescence emitted by the radiation is tuned near the S]/2, rnJ 2 Ps/2, the ion. ' In another experiment, quantum jumps were mj —'i transition frequency too. The atom cycles near- inferred from the statistics of the fluorescence emitted by ly continuously between these levels since the dipole selec- neutral atoms in a weak beam. In these experiments, the tion rules allow spontaneous decay only to the original quantum jump was a transition (either stimulated or ground level. A steady stream of fluorescence photons, spontaneous) into or out of a metastable excited state. which are readily detected, is emitted by the atom during In this paper, we report the observation of quantum this period. However, if the radiation is linearly polarized jumps due solely to spontaneous Raman transitions into with the polarization direction perpendicular to the direc- —' and out of ground-state sublevels. As opposed to the ear- tion of the magnetic field, the S]/2 tnj —, P3/2, ' lier experiments, we quantitatively compare the predic- rtt j —, transition is also allowed, although it is far from tions of the theory with the experiment. A particular real- resonance. This transition is indicated by the dashed ar- ization of the process is illustrated in Fig. l. It employs row in Fig. l. A spontaneous decay from the upper ' just one radiation source which is tuned between a pair of rnJ —, level can then leave the atom in the rrtj Zeeman levels of an atom or ion with a S]/2 ground state ground leveL This spontaneous Raman transition into the rnj 2 ground level takes the atom out of the —' ——' mj —, ms , cycling loop, causing the emitted fluorescence to suddenly stop. The off-resonant S]/2, i 1 —1 ttt J + 2 P3/p, ttt J 2 S]/2 tttJ 2 spontane- ous Raman transition (not shown in Fig. 1) will return the atom to the cycling loop where it will resume scattering. In a previous paper, we calculated the behavior of this system when the magnetic field strength is large enough t"at tt» y, 0, 4, where ha/2 is the energy separation be- tween adjacent excited-state sublevels, 3h, tt/4 is the sepa- ration between the ground-state sublevels, y is the excit- ed-state spontaneous decay rate, 0 is the on-resonance — Rabi frequency for the S]/2, rtt J 2 P3/2, ttt J transition, and b, to —too (see Fig. 1). We have used a single Mg+ ion confined by the static magnetic and electric fields of a Penning trap7 to demon- strate this process. The magnetic field for the data l2 presented here was 1.39 T which gives tt (2tt) 52 8) GHz=1200y, where y (2tr)43 MHz. Therefore, the t2 condition a» y, Q, L]] is quite readily achieved in our ex- periment. FIG. 1. The encrgy-level structure of the SI/2 and P3/g states For the trap used in this work (Fig. 2), we achieved a of an atom in a magnetic field (not to scale). A laser of frequen- large collection soi]d angle ( & 1% of 4tt sr), compared to cy QP is assumed to bc tuned near thc S~/2, 82J 2 I 3/2, an earher apparatus, by splitting the ring electrode into 111J 2 transition frequency mo. The energy separation of ad- two halves in the plane perpendicular to the magnetic 6eld jacent P3/2 (S]/q) sublevels is ha/2 (3ha/4). The indicated direction. The relative trap dimensions were chosen, Lorcntzian widths and detuning 6,, which are much less than a, with the aid of a computer, to make the potential nearly have been exaggerated for clarity. quadratic at the trap center. The pressure of back- Work of the U.S. Government Not Subject to U.S. Copyright PRECISE TEST OF QUANTUM JUMP THEORY 4545 100 ELECTRON FILAMENT 100 COMPENSATION ELECTRODE ,00000, ' 160 240 e (ms) 0 0 4 8 12 16 20 COMPENSATION Off duration ELECTRODE (ms) Mg OPEN FIG. 3. A histogram of the duration of fluorescence-off periods for a data run. The number of off periods which have a FIG. 2. Cross-sectional drawing of the Penning trap used in particular duration are plotted vs the duration. This data run the experiment. The shaded regions are ceramic support rods. had 512 off periods in 20 s. The solid line is a 6t of the data to The end-cap separation is 1.38 cm and the inner diameter of the Eq. (2). Inset: A portion of a data run showing quantum jumps ring electrode is 1.63 cm. The two ring electrodes and the two in fluorescence F as a function of time. compensation electrodes were grounded and the two end caps were at +12 V for this experiment. levels via spontaneous Raman transitions. For other realizations of quantum jumps, the dynamics ground gas in the apparatus was less than 10 Pa. of the population evolution and, therefore, the statistics of The 3S&g to 3Py2 transition wavelength for Mg+ is the emitted fluorescence are governed by effective two- 280 nm. We generated up to 200 pW of 280-nm radia- ' state rate equations. That is, there are rates R+ and tion frequency doubling the output of a single-mode, by R —for the atom to make transitions out of or into the en- continuous-wave dye laser in a deuterated ammonium ergy levels which comprise the strongly fluorescing or dihydrogen-phosphate crystal. The frequency width of "on" system and the system of levels which comprise the this radiation was much less than the natural width of ' y "off" system. (R+) and (R ) ' are equal to the the transition. The laser beam was focused near the mean duration of the fluorescence on periods, (T,„), and center of the trap with a beam waist an=45 pm. The off periods, (T,tr), respectively. Although the system con- ions were laser cooled when LL and since the beam was (0, sidered here is substantially different than those investi- directed at an angle of 74' relative to the magnetic field gated before, it was shown in Ref. 6 that the dynamics of axis all of the ion's degrees of motion were cooled directly. this system should also be governed by effective two-state The equilibrium temperature of the ion was only a frac- rate equations. The expressions for the rates R and R+, tion of 1 K when 6= —y/2. " Under these conditions, the Doppler broadening of the transition frequency was much R+ -(T.„)-'-0'y/(18a'), less than y, as verified by a scan of the laser frequency, ' and the ion was confined to dimensions which were much R — (T ff) 80 y/(9a ) less than u n. In order to laser cool in a Penning trap, it is necessary to position the center of the laser beam radially are simple because of the off-resonance nature of the exci- outward from the trap axis. " With a displacement of ap- tation, in contrast with the previously considered sys- ' proximatel~ 20 pm and our value of tvo, the saturation pa- tems. rameter 0 /y2 was equal to 1 at the position of the ion for A consequence of this type of dynamics is that the dis- a laser power of approximately 50 pW. From the tribution of fluorescence-on and fluorescence-off times definitions of Ref. 6, the ion spends twice as much time in should be exponential. In Fig. 3, we plot the duration of ' the ground mj ——, sublevel as in the excited mj fluorescence-off periods versus the number of periods in the data run which level when 0 y and 6 0. The fluorescence photons are off for this duration. The solid line were collected in a direction perpendicular to both the is a fit to the equation magnetic field and laser beam directions focusing onto by 8;a(r) -(T,s) 'exp( —t/(T, tr)) . a photomultiplier tube. The maximum detected photon count rate was 2X 10 /s for a single ion. The data are consistent with a distribution of this form. Data exhibiting quantum jumps are displayed in the in- An important prediction of Ref. 6 is that the ratio of the set in Fig. 3. The horizontal axis is divided into time in- mean duration of the fluorescence-on periods to the mean tervals of 0.5 ms duration. The vertical axis indicates the duration of the fluorescence-off periods should be a value number of photons counted during each time interval and which is only very weakly dependent on the variable pa- the points representing each interval are connected by rameters of the system, such as laser power and frequen- straight lines.
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