VOLUME 75, NUMBER 22 PHYSICAL REVIEW LETTERS 27NOVEMBER 1995

Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland Time and Frequency Division, National Institute of Standards and Technology, Boulder, Colorado 80303

P. Gould Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (Received 19 December 1994) We report laser cooling of a single 9Be1 ion held in a rf (Paul) ion trap to where it occupies the quantum-mechanical ground state of motion. With the use of resolved-sideband stimulated Raman cooling, the zero point of motion is achieved 98% of the time in 1D and 92% of the time in 3D. Cooling to the zero-point energy appears to be a crucial prerequisite for future experiments such as the realization of simple quantum logic gates applicable to quantum computation.

PACS numbers: 32.80.Pj, 42.50.Vk, 42.65.Dr

Dramatic progress in the field of atomic laser cooling We cool a single beryllium ion bound in a rf (Paul) ion has provided cooling of free or weakly bound atoms trap to near the zero-point energy using resolved-sideband to temperatures near the Doppler cooling limit [1], near laser cooling with stimulated Raman transitions along the photon recoil limit [2], and, more recently, below the lines suggested in Ref. [6]. The idea of resolved- the photon recoil limit [3,4]. For a tightly bound atom, sideband laser cooling with a single-photon transition is as a more natural energy scale is given by the quantized follows [12]. Consider a two-level atom characterized by 1 vibrational level n, where the energy is E ෇ h¯vy͑n 1 2 ͒ resonant transition frequency v0 and radiative linewidth for an atom confined in a harmonic potential of frequency g. We assume the atom is confined by a 1D harmonic vy . In this case, the fundamental cooling limit is the well of vibration frequency vy ¿ g. If a laser beam n ෇ 0 zero-point energy of the binding potential. In this (frequency vL) is incident along the direction of the Letter, we demonstrate a new technique for laser cooling atomic motion, the absorption spectrum is composed a trapped atom to the 3D zero-point energy. of a “carrier” at frequency v0 and resolved frequency- Attainment of the 3D ground state is significant for two modulation sidebands spaced by vy, which are generated primary reasons: (i) it appears to be a goal of intrinsic from the Doppler effect. Cooling occurs if the laser is interest as it is the fundamental limit of cooling for tuned to a lower sideband, for example, at vL ෇ v0 2 a bound atom and approaches the ideal of an isolated vy. In this case, photons of energy h¯͑v0 2vy͒ are particle at rest and (ii) it will be important in future absorbed and spontaneously emitted photons of average planned experiments. For example, once the ion is cooled energy h¯v0 return the atom to its initial internal state to the n ෇ 0 state, it should be possible to realize the thereby reducing the atom’s kinetic energy by h¯vy per Jaynes-Cummings interaction [5] in the regime of strong scattering even (assuming h¯vy is much greater than the coupling and generate other nonclassical states of motion photon recoil energy). Cooling proceeds until the atom’s such as squeezed states [6–8]. If the collective motion mean vibrational quantum number in the harmonic well is 2 of two or more trapped ions can be cooled to the zero given by ͗n͘min Ӎ͑g͞2vy͒ ø1[1,13]. The interaction point, it may be possible to transfer correlation from the with the laser is significantly reduced once in the n ෇ 0 external motional state to the internal spin state of the state; thus the zero-point state satisfies the operational ions. Generating “EPR”-like atomic spin states would not definition of a dark state [14] for g͞vy sufficiently small. only be interesting from the point of view of quantum Resolved-sideband cooling in 2D was previously achieved measurements [9], but may also allow a reduction of on a 198Hg1 ion using a narrow single-photon optical quantum noise in spectroscopy [6,7]. Zero-point cooling quadrupole transition [15]. combined with long coherence times may make it possible For laser cooling with stimulated Raman transitions to construct a quantum computer [10]. Cirac and Zoller [4,6,16,17], the single-photon transition is replaced by have proposed a quantum computer based on a system of a stimulated Raman transition between metastable levels trapped ions, in which information is stored in the spin (e.g., hyperfine or Zeeman electronic ground state), and and motional states of the ions [11]. The fundamental spontaneous Raman transitions irreversibly recycle the in- switching action in this implementation of a quantum ternal state of the atom. Stimulated Raman cooling of- computer is a coherent exchange between the spin state of fers the important practical advantages that the cooling an individual ion and a collective vibrational state of all linewidth can be varied experimentally, and the effective the ions. Cooling to the zero-point energy and realizing laser linewidth can be made very narrow by the use of the Jaynes-Cummings coupling is critical to this scheme. optical frequency modulators. These features of stimu-

0031-9007͞95͞75(22)͞4011(4)$06.00 © 1995 The American Physical Society 4011 VOLUME 75, NUMBER 22 PHYSICAL REVIEW LETTERS 27NOVEMBER 1995 lated Raman cooling have already been used to achieve very low temperatures for free or weakly bound neutral atoms in the unresolved-sideband limit [4]. Since narrow single-photon transitions are not required, the resolved- sideband Raman cooling technique described here can be generalized to many ion species and may also be applied to strongly bound neutral atoms held in dipole traps [18] and optical lattices [19]. The experiment is conducted as follows. We first achieve ͗ny͘Ӎ1 in 3D ͑y ෇ x, y, z͒ by performing Doppler cooling on an allowed electric dipole transition (g large) and making the trap strong enough that vy Ӎ g. FIG. 1. (a) Laser beam geometry. The trap ring electrode This Doppler “precooling” places the ion into the Lamb- ± Dicke regime (Dx ø l 2p, where Dx is the rms spread (in the x-y plane) is shown rotated 45 into the page ͞ (the endcap electrodes along the z axis are not shown; see of the ion position and l is the wavelength of the dipole Ref. [20]).p A magnetic field B defines a quantization axis transition). We reduce ͗ny͘ further in 3D by employing along xˆ͞ 2 1 yˆ͞2 1 zˆ͞2, and laser beam polarizations are a second stage of cooling on narrower Raman transitions indicated. Fluorescence light is collected along the direction 9 1 between hyperfine ground states ͑gRam ø vy͒. Finally perpendicular to the page. (b) Relevant Be energy levels (not to scale), indicated by F, mF , quantum numbers in the we extract ͗ny͘ by measuring the asymmetry of the 2 2 S1͞2 ground state ( P fine-structure splitting is Ӎ197 GHz, resolved motional sidebands in the Raman absorption 2 2 S1͞2 hyperfine splitting is v0͞2p Ӎ 1.250 GHz, and the P3͞2 spectrum [15]. hyperfine and Zeeman structure is not resolved). All optical 9 1 A single Be ion is stored in a coaxial-resonator-based transitions are near l Ӎ 313 nm. D1 and D2: Doppler rf (Paul) ion trap (r0 Ӎ 170 mm, z0 Ӎ 130 mm) described precooling and detection beams; D3: j2, 1͘ depletion beam; R1 and R2: Raman beams. The detuning of R1 and R2 from the in Ref. [20]. A potential V0 cos͑V0t͒ is applied to the ring 2 2 9 1 S1͞2 ! P1͞2 transition is D͞2p Ӎ 12 GHz. (V0 Ӎ 600 V, V0͞2p Ӎ 231 MHz), yielding Be pseu- dopotential oscillation frequencies of ͑vx, vy, vz͒͞2p Ӎ ͑11.2, 18.2, 29.8) MHz along the principal axes of the trap [21]. Once a 9Be1 ion is loaded in the trap, its lifetime is beam. The difference frequency of the Raman beams about 6 h (background pressure ,1028 Pa). is tunable over the range 1200–1300 MHz with the use The geometry and polarizations of the various laser of a double-pass acousto-optic modulator (AOM). The beams as well as the relevant energy levels in 9Be1 are counterpropagating Raman beams are also at oblique summarized in Fig. 1. The quantization axis is defined angles to the trap’s principal axes and are therefore by an applied magnetic field jBj Ӎ 0.18 mT. Laser sensitive to motion in all dimensions. All beams are radiation (beam D2, s1 polarized) detuned slightly to shuttered with AOMs. The 313 nm fluorescence from the 2 2 the red of the S1͞2͑F ෇ 2͒ ! P3͞2 transitions (l Ӎ trapped ion is imaged through f͞2 optics onto a position- 2 313 nm, g͞2p Ӎ 19.4 MHz, P3͞2 hyperfine structure sensitive photomultiplier tube, resulting in a photon count Ӎ1 MHz) is directed at oblique angles to all the principal rate as high as Ӎ10 kHz (quantum efficiency Ӎ2 3 axes of the trap, providing Doppler precooling in all trap 1024). The background count rate is Ӎ100 Hz. dimensions. A second 313 nm source (beam D1, s1 Doppler precooling, Raman cooling, and measurement 2 2 polarized) tuned to the S1͞2͑F ෇ 1͒ ! P3͞2 transition of the Raman absorption spectrum are accomplished prevents optical pumping to the F ෇ 1 ground state. by following the sequence outlined in Table I. After A pair of Raman beams is also directed into the trap precooling (beams D1, D2, and D3), the ion is prepared 2 (beams R1 and R2) to drive a much narrower transition in the S1͞2j2, 2͘ electronic ground state by turning off 2 between the S1͞2 jF ෇ 2͘ and jF ෇ 1͘ hyperfine ground beam D2. The relative tuning of the Raman beams is set 9 1 2 states of Be through the virtual P1͞2 state. The to a first lower (red) sideband near v0 2vy, driving a Raman beams are detuned Ӎ12 GHz to the red of stimulated Raman transition from the j2, 2͘ jny͘ state to 2 2 the S1͞2 ! P1͞2 transition with a difference frequency the j1, 1͘jny 2 1͘ state. The ion is then recycled with 2 very near the S1͞2 hyperfine splitting of v0͞2p Ӎ nearly resonant beams D1 and D3, inducing spontaneous 1 1.250 GHz. A third 313 nm source (beam D3, s Raman transitions predominantly to the j2, 2͘ jny 2 1͘ 2 2 polarized) is tuned to the S1͞2͑F ෇ 2͒ ! P1͞2͑F ෇ 2͒ state. This cycling of stimulated and spontaneous Raman transition and depletes the jF, mF͘ ෇ j2, 1͘ ground state. transitions (steps 3 and 4 of Table I) is repeated as desired Beams D1, D2, and D3 are derived from two frequency- on any or all of the three dimensions. The relative doubled dye lasers, producing 5–10 mW of power in tuning of the Raman beams is then set near v0 1dpr, each beam, enough to saturate the ion near resonance. and a stimulated Raman “probe” transition is driven Beams R1 and R2 are derived from a third frequency- between the states, where Dny ෇ 0, 61. The probability doubled dye laser, providing a few mW of power in each of driving the probe transition is then measured by

4012 VOLUME 75, NUMBER 22 PHYSICAL REVIEW LETTERS 27NOVEMBER 1995 driving a stimulated Raman “exchange p pulse” from j2, 2͘ jny͘ $j1, 1͘jny͘, followed by driving the cycling 2 2 S1͞2j2, 2͘ ! P3͞2j3, 3͘ transition with beam D2 and gating and collecting the fluorescence. (The exchange p pulse in step 6 of the table reduces the fluorescence noise when ͗ny͘Ӎ0.) The ion scatters thousands of photons on the cycling transition before decaying into the j1, 1͘ electronic state due to imperfect circular polarization of beam D2, resulting in a net quantum efficiency near 1. As this sequence is repeated at Ӎ4 kHz, d is slowly pr FIG. 2. Raman absorption spectrum of a single 9Be1 ion swept, yielding the Raman absorption spectrum. after Doppler precooling (solid points) and after five cycles The Raman carrier represents the transition j2, 2͘ jny͘ $ of additional resolved sideband stimulated Raman cooling on j1, 1͘jny͘ and occurs at dpr ϵ 0 (compensating for sta- the x dimension (hollow points). The observed count rate ble Zeeman and ac Stark shifts of Ӎ2 MHz). In the is normalized to the probability P͕j2, 2͖͘ of the ion being in the j2, 2͘ state. The first blue and red sidebands of the Lamb-Dicke regime, the carrier feature has strength Ic ෇ 2 x dimension are shown at dpr ͞2p Ӎ 611.2 MHz. Similar sin ͑Vtpr ͒, where V ෇ g1g2͞D is the carrier Rabi flop- sidebands are found near 618.2 MHz (y dimension) and at ping frequency, tpr is the exposure time of the atom to 629.8 MHz (z dimension). For precooling, the asymmetry in the probe Raman beams, g1 and g2 are the resonant Rabi the sidebands indicates a thermal average vibrational occupation frequencies of Raman beams R1 and R2, and D is the number of ͗nx͘Ӎ0.47͑5͒. For Raman cooling, the reduction detuning of the Raman beams from the excited state (we of the red sideband and growth of the blue sideband implies further Raman cooling in the x dimension to ͗nx͘Ӎ0.014͑10͒. assume D ¿ g, g1, g2) [6]. In each dimension, blue and The widths of the features are consistent with the 2.5 ms red sidebands occurring at dpr ෇ 6vy represent the tran- Raman probe time. Each point represents an average of 400 sitions j2, 2͘ jny͘ $j1, 1͘jny 6 1͘. The strengths of the measurements, corresponding to Ӎ5 min of integration time for blue and red sidebands in the Lamb-Dicke regime are the entire data set. The lines connect the data points. blue 2 1͞2 red given by Iy ෇ ͗sin ͓Vtpr hy͑ny 1 1͒ ͔͘ and Iy ෇ 2 1͞2 ͗sin ͓Vtpr hyny ͔͘, where the average is performed over the distribution of ny. The Lamb-Dicke parameters are ployed (steps 3 and 4 of Table I with vy ෇ vx). The given by hy ෇ dkyry ෇ ͑0.21, 0.12, 0.09), where dky ෇ exposure time tRam of the last Raman pulse is set so 2ky is the component of the difference in the counterprop- that VtRamhx Ӎ p͞2 or tRam Ӎ 2.5 ms, corresponding agating Raman beam wave vectors in the yth dimension, to nearly a p pulse from the nx ෇ 1 state to the nx ෇ 0 1͞2 and ry ෇ ͑h¯͞2mvy͒ is the spread of the ny ෇ 0 wave state. The durations of the earlier pulses are set shorter function. The sideband Rabi flopping frequencies Vhy to optimize the cooling. The recycle time between each are typically a few hundred kilohertz, thus the absorption stimulated Raman transition is about 7 ms, ample time features are well resolved and spontaneous emission dur- for the ion to scatter the expected average of Ӎ3 photons ing all stimulated Raman processes is negligible. from beams D1 and D3 and ultimately get recycled to A Raman absorption spectrum of the first blue and red the j2, 2͘ state. The suppression of the red sideband sidebands of the x direction ͑dpr ෇ 6v͒ is shown in Fig. 2 (and growth of the blue sideband) indicates the extent (solid points) for Doppler precooling only (omitting steps of the additional cooling, from ͗nx͘Ӎ0.47 to ͗nx͘Ӎ 3 and 4 in Table I). Similar features appear at dpr ෇ 6vy 0.014͑10͒ (the nx ෇ 0 state is occupied Ӎ98% of the and 6vz.Ifnyis thermally distributed, then it is straight- time). We observe no further cooling by increasing red blue forward to show that Iy ͞Iy ෇ ͗ny͑͘͞1 1 ͗ny͒͘, inde- the number of Raman cooling cycles beyond about five pendent of Vtpr hy . By recording several spectra varying and see little sensitivity to the details of the Raman tpr , we find the ratio of red to blue sideband strength re- cooling pulse durations. As discussed above, we verify mains approximately constant, indicating a nearly thermal that the distribution of ny is nearly thermal after Raman distribution of ny. (We ensure that V is the same on the cooling. We achieve resolved-sideband Raman cooling blue and red sidebands.) We measure ͗ny͘ for a variety in 3D by sequentially driving on all three red sidebands. of red detunings of Doppler precooling beams D1 and D2 Five cycles of cooling are applied to each dimension and obtain values as low as ͗ny͘Ӎ͑0.47, 0.30, 0.18) in the (order xyzxyz ...) by alternating the tuning of the Raman three dimensions at a detuning of about 230 MHz (we es- cooling beams between the three red sidebands. From timate Ӎ10% uncertainties in the measurements). At other the measured asymmetry of each pair of sidebands, we detunings, we measure values as high as ͗ny͘Ӎ7. These infer 3D Raman cooling to ͗ny͘Ӎ͑0.033, 0.022, 0.029), values and their behavior with detuning are consistent with or the nx ෇ ny ෇ nz ෇ 0 3D ground state being occupied the theoretical limit of Doppler cooling [17]. Ӎ92% of the time. Figure 2 includes a Raman absorption spectrum follow- The limit of Raman cooling is determined by heating ing additional sideband Raman cooling (hollow points). from off-resonant stimulated-Raman transitions [expected 2 2 Five Raman cooling cycles in the x dimensions are em- to result in a limit of ͗nx͘St Ram Ӎ͑g1g2͒͑͞vyD͒ Ӎ

4013 VOLUME 75, NUMBER 22 PHYSICAL REVIEW LETTERS 27NOVEMBER 1995

TABLE I. Timing sequence for Doppler precooling, resolved-sideband stimulated Raman cooling and Raman detection of ͗ny͘. As the sequence is repeated through steps 1–7, dpr is slowly swept across absorption features. Raman cooling steps (3 and 4) are repeated as desired within the sequence.

Duration Beams Raman Step (ms) D1, D3 D2 R1, R2 tunning Function

1 Ӎ50 On On Off ··· Doppler precool 2 Ӎ7 On Off Off ··· Prepare in j2, 2͘ state 3 1–3 Off Off On v0 2vy Stimulated Raman transition j2, 2͘jny ͘ !j1, 1͘jny 2 1͘ 4 Ӎ7 On Off Off ··· Spontaneous Raman recycle j1, 1͘jny 2 1͘ !j2, 2͘jny 2 1͘ 0 5 1–3 Off Off On v0 1dpr Probe ͗ny ͘ with stimulated Raman transitions j2, 2͘jny ͘ !j1, 1͘jny͘ 6 Ӎ1 Off Off On v0 Exchange p pulse: j2, 2͘jny ͘ $j1, 1͘jny͘ 7 Ӎ200 Off On Off ··· Detect transition in step 5: cycle on j2, 2͘ !j3, 3͘; collect fluorescence

1023] and heating from off-resonant spontaneous emis- 1995), p. 450, and references therein. sion from the Raman beams [a limit of ͗nx͘Sp Ram Ӎ [11] J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 2 23 ͑g1g2͞D ͒hxgtRam Ӎ 10 ]. We believe the minimum (1995). [12] D. J. Wineland and H. Dehmelt, Bull. Am. Phys. Soc. 20, measured value of ͗nx͘Ӎ0.02 may be due to anomalous heating of the ion, which we measure to be ≠͗n͘͞≠t Ӎ 637 (1975). [13] W. Neuhauser, M. Hohenstatt, P. Toschek, and H. 11͞msec by inserting various amounts of time between Dehmelt, Phys. Rev. Lett. 41, 233 (1978). cooling probing. We are currently investigating the [14] R. Dum, P. Marte, T. Pellizari, and P. Zoller, Phys. Rev. source of this heating. Lett. 73, 2829 (1994). This work is supported by the Office of Naval Research [15] F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. and the Army Research Office. We acknowledge consid- Wineland, Phys. Rev. Lett. 62, 403 (1989). erable contributions from J. C. Bergquist. We thank N. R. [16] P. E. Toschek, Phys. (Paris) 10, 761 (1985); H. Dehmelt, Newbury, J. D. Miller, and M. Young for comments on G. Janik, and W. Nagourney, Bull. Am. Phys. Soc. 30, 111 the manuscript. (1985); B. Appasamy, I. Siemers, Y. Stalgies, J. Eschner, R. Blatt, W. Neuhauser, and P. E. Toschek, Appl. Phys. B 60, 473 (1995). [17] M. Lindberg and J. Javanainen, J. Opt. Soc. Am. B 3, [1] D. J. Wineland and W. M. Itano, Phys. Today 40, No. 6, 1008 (1986). 34 (1987). [18] S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, Phys. [2] C. Cohen-Tannoudji and W. D. Phillips, Phys. Today 43, Rev. Lett. 57, 314 (1986); W. D. Phillips, in Laser No. 10, 33 (1990). Manipalation of Atoms and Ions, Proceedings of the [3] A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and International School of Physics “Enrico Fermi,” Varenna, C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. 1991, edited by E. Arimondo and W. D. Phillips (North- Lawall, F. Bardou, B. Saubamea, M. Leduc, A. Aspect, Holland, Amsterdam, 1992), p. 325; J. D. Miller, R. A. and C. Cohen-Tannoudji, Phys. Rev. Lett. 73, 1915 Cline, and D. J. Heinzen, Phys. Rev. A 47, R4567 (1993). (1994). [19] P. Verkerk, B. Lounis, C. Salomon, and C. Cohen- [4] M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992); Tannoudji, Phys. Rev. Lett. 68, 3861 (1992); P. Jessen, C. H. Lee, C. Adams, N. Davidson, B. Young, M. Weitz, M. Gerz, P. Lett, W. Phillips, S. Rolston, R. Spreeuw, and C. Kasevich, and S. Chu, in Atomic Physics XIV, edited by Westbrook, Phys. Rev. Lett. 69, 49 (1992); A. Hemmerich D. J. Wineland, C. E. Wieman, and S. J. Smith (AIP Press, and T. Hänsch, Phys. Rev. Lett. 70, 410 (1993). New York, 1995), p. 258. [20] S. R. Jefferts, C. Monroe, E. Bell, and D. J. Wineland, [5] E. T. Jaynes and C. W. Cummings, Proc. IEEE 51,89 Phys. Rev. A 51, 3112 (1995). (1963). [21] The drive frequency V0 Ӎ 231 MHz is much larger [6] D. J. Heinzen and D. J. Wineland, Phys. Rev. A 42, 2977 than the pseudopotential vibration frequencies vy, so the (1990). contribution of the driven “micromotion” at V0 to the [7] D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. overall amplitude of the ion motion is very small. This Heinzen, Phys. Rev. A 50, 67 (1994). includes the micromotion induced form static background [8] J. I. Cirac, A. S. Parkins, R. Blatt, and P. Zoller, Phys. Rev. fields, which are minimized with compensation electrodes Lett. 70, 556 (1993); J. I. Cirac, R. Blatt, A. S. Parkins, (see Ref. [20]). Moreover the small FM micromotion and P. Zoller, Phys. Rev. Lett. 70, 762 (1993). sidebands at 6V0 are well resolved ͑V0 ¿ g͒ and far [9] D. M. Greenberger, M. A. Horne, and A. Zeilinger, Phys. from the region of interest in the absorption spectrum. Today 46, No. 8, 22 (1993). Thus the trap can be accurately approximated as a simple [10] A. Ekert, in Atomic Physics XIV, edited by D. J. Wineland, harmonic oscillator with frequencies vy . C. E. Wieman, and S. J. Smith (AIP Press, New York,

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