Integrating cavity quantum electrodynamics and ultracold-atom chips with on-chip dielectric mirrors and temperature stabilization
aa r X i v : . [ qu a n t - ph ] J u l Integrating cavity quantum electrodynamics and ultracold-atom chips with on-chipdielectric mirrors and temperature stabilization
T.P. Purdy ∗ and D.M. Stamper-Kurn Department of Physics, University of California, Berkeley CA 94720 (Dated: July 1, 2007)We have fabricated an atom chip device which combines the circuitry for magnetic trapping ofcold atoms with high-finesse optical resonators suitable for cavity QED in the single-atom strongcoupling regime. Fabry-Perot optical resonators with finesse
F ≥ × were formed betweena micropatterned on-chip planar mirror with lateral dimension of ≤ µ m and a curved mirrorsuspended above the chip. The strong and rapid thermal coupling between on-chip electrical andoptical elements was utilized to stabilize the cavity mirror separation with servo bandwidth exceeding100 kHz during simulated operation of the atom chip.PACS 42.50.Pq; 03.75.Be; 42.82.Cr Atom chips [1, 2, 3, 4, 5], which incorporate micro-fabricated electromagnets, electrodes and magnetic ma-terials to trap atoms in vacuum above the chip surface,stand to expand the scientific reach of ultracold atomicgases. Given that optical manipulation and detection isessential to many ultracold atom experiments, the util-ity of atom chips is enhanced by the addition of opticalelements onto the chips.In particular, on-chip optical resonators would allowfor highly sensitive, high bandwidth, and localized de-tection of atoms, improving the precision and allowingexplorations of quantum-limited measurements. Low-finesse cavities can improve detection sensitivity [6] evento the single atom level [7, 8, 9, 10], although such de-tection is destructive in that detected atoms are per-force heated or changed in their internal state. In con-trast, higher finesse cavities with small mode size enable nondestructive atom detection at the single atom level,provided that the single-atom strong coupling regime( C ≫
1) is attained. Here, the single-atom cooperativityis defined as C = g / κ Γ, where g is the vacuum Rabi fre-quency, and κ and Γ are the cavity and atomic coherencedecay rates, respectively. Indeed, in this regime, myr-iad protocols based on cavity quantum electrodynamics(CQED) allow an interface between material and opticalrepresentations of quantum information.Several approaches have been pursued for achievingthe strong-coupling regime of CQED in a manner com-patible with magnetic or optical micromanipulation ofultracold atoms. Fabry-Perot resonators have been havebeen employed in atom chip experiments using both con-ventional macroscopic [10] and novel microscopic [6] mir-rors, attaining cooperativity as high as C = 2 .
1. Othermicroscopic Fabry-Perot resonators with higher coop-erativity have also been constructed [11, 12]. Singleatoms have been detected using monolithic microtoroidresonators [13], and resonators employing artificial pho-tonic bandgap materials [14] have been fabricated; bothachieve the strong coupling regime and, in principle, are ∗ Electronic address: [email protected] (cid:11)(cid:69)(cid:12)(cid:54)(cid:68)(cid:83)(cid:83)(cid:75)(cid:76)(cid:85)(cid:72) (cid:38)(cid:82)(cid:83)(cid:83)(cid:72)(cid:85) (cid:51)(cid:79)(cid:68)(cid:87)(cid:76)(cid:81)(cid:88)(cid:80) (cid:50)(cid:81)(cid:16)(cid:70)(cid:75)(cid:76)(cid:83)(cid:48)(cid:76)(cid:85)(cid:85)(cid:82)(cid:85)(cid:38)(cid:68)(cid:89)(cid:76)(cid:87)(cid:92)(cid:48)(cid:82)(cid:71)(cid:72) (cid:54)(cid:76)(cid:50) (cid:21) (cid:11)(cid:68)(cid:12) (cid:51)(cid:85)(cid:82)(cid:69)(cid:72)(cid:47)(cid:68)(cid:86)(cid:72)(cid:85)(cid:38)(cid:88)(cid:85)(cid:89)(cid:72)(cid:71)(cid:48)(cid:76)(cid:85)(cid:85)(cid:82)(cid:85) (cid:21)(cid:19)(cid:19)(cid:3)(cid:541)(cid:80) (cid:11)(cid:76)(cid:12) (cid:3)(cid:11)(cid:76)(cid:76)(cid:12) (cid:3)(cid:11)(cid:76)(cid:89)(cid:12)(cid:3)(cid:11)(cid:76)(cid:76)(cid:76)(cid:12)
FIG. 1: (a) A CQED/atom chip includes electromagnet wiresand a small planar mirror microfabricated on a sapphire sub-strate. A curved mirror suspended above the chip completesa vertically oriented Fabry-Perot resonator in the strong-coupling regime of CQED. (b) Microscope image of finisheddevice with inset schematic showing portions of the platinumlayer obscured in the photograph. (i) thermometer wire, (ii)dielectric mirror pad, (iii) heater wire, (iv) waveguide wire integrable with atom chip elements.Here, we describe a microfabricated CQED/atom chipcombining magnetic atom traps and a high-finesse Fabry-Perot cavity, with a single atom cooperativity of up to C = 50 for the Rb D2 transition at a wavelength λ = 780 nm. The cavity utilizes an on-chip planar mirror,patterned with lateral dimensions of 100 µ m or below.The second, curved mirror that completes the cavity ismounted above the chip with its optical axis perpendic-ular to the chip surface (Fig. 1). Conductors are fabri-cated on the mirror substrate, creating a two-wire mag-netic waveguide and magnetic conveyor belt [15] strad-dling the on-chip mirror. Ohmic heating in these elec-tromagnet wires leads to substantial displacement of theon-chip mirror. However, we turn this strong thermalcoupling to an advantage as a means of deliberately ac-tuating the cavity mirror via an on-chip temperature sta-bilization circuit. The cavity resonance is thereby stabi-lized with a servo bandwidth exceeding 100 kHz. Ourmethods for microfabricating and rapidly actuating highreflectivity optics represent an advance in the miniatur-ization of optical components, with applications beyondultracold atom experiments.In designing the on-chip mirror, one encounters a co-incidence of length scales. On one hand, the typical ∼ w ∼ µ m for the optical mode supported by a cavitywith mirror spacing in the 10 – 100 µ m range. In orderto maintain a cavity finesse of F ≥ , a clear apertureof radius ≃ µ m is then required to limit diffractionlosses at the aperture edge. On the other hand, con-fining rubidium atoms magnetically to linear dimensions d ≪ λ , so that the coupling strength between the atomand the standing-wave cavity mode is well determined,requires that electromagnets be placed within 100 µ m ofthe atoms. Here, we assume the electromagnets operateat current densities of ∼ A/cm , a practical limit foratom chip wires [16]. This consideration sets a maximumsize for the clear aperture of the on-chip mirror.The CQED/atom chip fabrication starts with a twoinch diameter, 4 mm thick, c -axis cut sapphire wafer,which is superpolished on one surface and coated with ahigh reflectivity multilayer dielectric mirror coating con-sisting of alternating layers of SiO and Ta O (ResearchElectro-Optics, Boulder, CO). This mirror coating, withtotal thickness of over 5 µ m, was optimized for highest re-flectivity at 780 nm, and some samples were measured tohave total scattering, absorption, and transmission lossesbelow 10 ppm per reflection.Small on-chip mirrors were formed by etching away thehigh-reflectivity dielectric coating except in selected ar-eas that form the remaining “mirror pads.” To definethese pads and protect their surfaces from subsequentprocessing, a 400 nm layer of high purity aluminum wasfirst thermally evaporated onto the mirror surface. Thislayer was then patterned, and the exposed dielectric coat-ing was removed in a reactive ion, parallel plate plasmaetcher operating with 100 sccm CF and 10-20 sccm O ,at a pressure of about 85 mTorr and an RF power densityof about 0.4 W/cm , and with the chip at a temperatureof 120 ◦ C. Since the etch rate for sapphire was negligiblecompared to that for the dielectric layers (80 nm/min),such etching left exposed the flat substrate in all unpro-tected regions of the mirror. Lateral etching of about 5 µ m on the margins of the mirror pads was observed.To test the mirrors microfabricated in this manner, wepatterned a sapphire wafer with mirror pads of dimen-sions ranging between 40 and 250 µ m. The aluminummask was then removed using a commercial etchant.Fabry-Perot cavities were formed with each on-chip mir-ror using a 5 cm radius of curvature mirror positionedabove the chip surface. The cavity finesse was thenmeasured for varying cavity lengths by probing with a (cid:48)(cid:82)(cid:71)(cid:72)(cid:3)(cid:58)(cid:68)(cid:76)(cid:86)(cid:87)(cid:3)(cid:11)(cid:541)(cid:80)(cid:12) (cid:41) (cid:85) (cid:68) (cid:70) (cid:87) (cid:76) (cid:82)(cid:81)(cid:68) (cid:79) (cid:3) (cid:47)(cid:82) (cid:86)(cid:86) (cid:72) (cid:86) (cid:3) (cid:83)(cid:72) (cid:85) (cid:3)(cid:3)(cid:3) (cid:53) (cid:72) (cid:73) (cid:79) (cid:72) (cid:70) (cid:87) (cid:76) (cid:82)(cid:81) (cid:3) (cid:11) (cid:59) (cid:20)(cid:19) (cid:16) (cid:25) (cid:12) (cid:20)(cid:25)(cid:19)(cid:20)(cid:21)(cid:19)(cid:27)(cid:19)(cid:23)(cid:19)(cid:19) (cid:22)(cid:24)(cid:22)(cid:19)(cid:21)(cid:24)(cid:21)(cid:19) FIG. 2: Losses in microfabricated mirrors with nominal radiiof 50 (diamonds), 70 (triangles), and 100 µ m (squares) weremeasured for variable cavity mode waists. The 20 ppm to-tal losses per reflection from the on-chip mirror observed atthe smallest cavity spacing is consistent with that observedfor the mirror prior to microfabrication. Increased diffrac-tion losses at larger cavity spacing, with lines showing fits toa simple model, indicate effective mirror radii of 47 and 65 µ m for the two smallest mirrors, respectively, consistent withthe observed lateral etching of the mirror pads during theirfabrication. grating-stabilized diode laser at wavelengths near λ =780 nm . At the smallest cavity spacing, for which thesupported cavity mode had the narrowest waist, thesecavities attained a finesse of F ≥ × , equal to thatattained prior to microfabrication given the parameterstop curved mirror. The cooperativity of such cavitiesis about 50 for a 25 µ m mirror spacing. Here the fi-nesse is limited mainly by scattering and absorption inthe on-chip dielectric coating. We have, however, ob-tained sapphire wafers with higher quality mirror coat-ings. If such a wafer was employed as a CQED/atomchip, the finesse and cooperativity of the on-chip cavitywould be improved by at least a factor of two.As the spacing between the cavity mirrors was in-creased, the transverse waist of the supported cavitymode increased, and the cavity finesse was diminishedby diffraction losses off the edges of the on-chip mirror(Fig. 2). We quantify these losses per reflection as thefractional intensity of a Gaussian beam with 1 /e radius w that falls outside the effective radius a of the on-chipmirror. The total round-trip loss δ c = 2 π/ F is then givenas δ c = e − a /w + δ + δ where δ , δ are the remain-ing, spacing-independent loss of each of the two cavitymirrors. By fitting to this expression for δ c , we obtainedexperimentally the usable radius of each on-chip mirror.This was found to be 3 – 5 µ m smaller than the nomi-nal radius of the microfabricated mirror, consistent withthe observed lateral etching of the mirrors during theirmicroprocessing.The birefringence of the mirror coating was monitoredbefore and after processing. Circular mirror pads exhib-ited linear birefringent phase shifts of ≃ − rad perreflection, similar to those observed on the unprocessedmirrors. For mirror pads fabricated with a rectangularshape, the linear birefringence was increased to ≃ − rad, with principal axes correlated with the orientationof the rectangle. This effect was observed for mirror padsformed both on sapphire and on glass substrates, and isascribed to strains induced in the mirror coatings by theasymmetric mirror shape.In designing a complete CQED/atom chip incorporat-ing such mirror pads the inevitable thermal coupling ofthe mirrors to the current-carrying, heat-generating wireson the chip must be considered. To quantify this cou-pling we calculate the expected temperature variation T ( r, ω ) e − ıωt due to an AC heat source on the surfaceat a distance r and varying at angular frequency ω . Fora point heat source generating power P e − ıωt on the sur-face of a half space of material, we obtain as a solutionto the heat equation T ( r, ω ) = P πk e − p iωr α r (1)while for a line source generating power per length of A e − ıωt we find T ( ρ, ω ) = − iA k " J r − iωρ α ! − iY r − iωρ α ! (2)Here J and Y are Bessel functions of the first andsecond kind respectively, ρ is the distance to the line, k = 40 W / mK is the thermal conductivity of sapphire,and α = 1 . × − m / s is its thermal diffusivity.In the limit ω →
0, these expressions indicate thesteady-state temperature increase at the chip surface dur-ing its operation. For example, the DC temperature riseat a mirror pad located 100 µ m from copper wires run-ning 3 A through a 300 µ m wire cross section is esti-mated as 20 K. Under these conditions, the expansionof the substrate below the mirror would lift the mirrorsurface by about 125 nm. This displacement is enor-mous compared to the mirror displacement of λ/ F ≃ ω ≫ α/r ≃ π ×
200 s − the temper-ature response for both geometries is exponentially sup-pressed. For the example mentioned above this impliesa rapid timescale τ = r /α ≃ ≃
100 nm/ms that would berequired to actively stabilize the cavity resonance duringoperation of the atom chip presents a formidable techni-cal challenge.To address this challenge, elements for a high-speedtemperature stabilization circuit were fabricated as partof the CQED/atom chip. Platinum wire heaters and Re-sistance Temperature Detectors (RTD) were placed di-rectly onto the sapphire substrate, near the mirror, tomonitor and control the substrate surface temperature.The complete CQED/atom chip device (Fig. 1) wasfabricated in two steps. First, microfabricated mirrors were created using the process described above. Then,with mirror pads still protected by aluminum, standardatom-chip fabrication methods were employed [17] to pro-duce the heater, thermometer, and magnet wires on thesapphire substrate left bare by the previous plasma etch.The platinum RTD and heater wires, 100 nm thick,were patterned using electron beam evaporation and alift-off process. This method was found to be suitablefor patterning 5 µ m wide features within 10 µ m of themirror locations, despite steps of almost 6 µ m in heightfrom the sapphire substrate to the to surface of the mir-ror. Resistances of several kΩ were obtained in an areaas small as .04mm . A 1 µ m SiO was next applied tothe wafer via plasma enhanced chemical vapor deposi-tion, which requried the entire wafer to reach a temper-ature of 350 ◦ C. This layer insulated the platinum wiresfrom overlaid conducting layer and also partially insu-lated the electromagnet wires from the substrate, slow-ing the thermal coupling to the on-chip mirrors. Holeswere patterned through the SiO layer to make electricalcontacts between the platinum wires and overlaid cop-per leads. Copper magnet wires were electroplated to athickness of 5 – 10 µ m through a photoresist mold. Fi-nally the mirror surfaces were uncovered via a wet etch,and the finished wafer was cleaned in acetone, isopropylalcohol, and deionized water.The operation of this CQED/atom chip was tested un-der conditions simulating the operation of the chip incold-atom experiment. A Fabry-Perot cavity was con-structed as before, employing the on-chip mirror sur-rounded by platinum and copper wires. The wholeassembly was mounted on a vibration isolated copperheatsink, and measurements were performed in open air.The optical cavity was stabilized by monitoring thetransmission of a probe laser and feeding back to eithera piezoelectric transducer (PZT) that displaced the topmirror or the platinum heater that displaced the on-chipmirror. Following the example of other CQED exper-iments [18, 19], the cavity was probed with laser lightfar detuned from the atomic transitions of rubidium. Atthis laser wavelength of 850 nm, the cavity linewidth wasabout 10 times larger than at 780 nm. Thus we requiredthat the cavity resonance be maintained to just a fewpercent of its linewidth at 850 nm.We tested three different schemes for stabilizing thecavity during rapid variations of currents in the mag-netic waveguide wires. In the first scheme, we stabilizedthe temperature, as measured by the RTD, using theheater wire, while independently stabilizing the cavitytransmission using PZT actuation of the curved mirror.While the temperature stabilization operated with servobandwidth of several kHz, we found that the response ofthe cavity resonance to varying thermal conditions wasonly moderately diminished by this stabilization (Fig. 3).A second stabilization scheme added a feed-forwardcomponent to the method described above. Here, a sig-nal proportional to the magnet wire current was filtered,inverted, offset, and fed into the heater wire. This feed- (cid:11)(cid:76)(cid:12)(cid:11)(cid:76)(cid:76)(cid:12)(cid:11)(cid:76)(cid:76)(cid:76)(cid:12) (cid:16)(cid:27)(cid:16)(cid:23)(cid:19) (cid:40) (cid:73)(cid:73) (cid:72) (cid:70) (cid:87) (cid:76) (cid:89) (cid:72) (cid:3) (cid:48) (cid:76) (cid:85)(cid:85) (cid:82) (cid:85) (cid:39) (cid:76) (cid:86) (cid:83) (cid:79) (cid:68) (cid:70) (cid:72) (cid:80) (cid:72)(cid:81) (cid:87)(cid:3) (cid:11) (cid:81) (cid:80) (cid:12) (cid:21)(cid:19)(cid:20)(cid:19)(cid:19) (cid:87)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11)(cid:80)(cid:86)(cid:12) FIG. 3: Response of cavity resonance to an 0.5 A current pulsethrough the waveguide wires. The PZT voltage necessary tostabilize the cavity resonance, indicative of thermally induceddisplacements of the on-chip mirror, is recorded when theheater wire is either (i) not used, (ii) used to feedback totemperature variations measured at the RTD, or (iii) used ina feed-forward scheme. forward scheme was tuned so as to suppress the responseof the cavity to rapid thermal changes by over an or-der of magnitude for a short time after the magnet wirecurrents were switched.The most successful stabilization scheme employed acombination of both PZT and thermal actuation of thetwo cavity mirrors to stabilize directly the optical cavityresonance. The response of the cavity resonance positionto actuation by the on-chip heater showed the expectedroll off in frequency starting at 200Hz, but maintaineda smooth feedback phase beyond 200 kHz, showing nodiscernible coupling to mechanical resonances. Remark-ably, we were thus able to apply straightforward thermalfeedback with servo bandwidth of over 100 kHz.As shown in Fig. 4, this last stabilization schemestrongly suppressed both rapid transients and slow driftof the cavity resonance frequency (i.e. the effective cav-ity spacing) in response to the switching heat loads of anoperational atom chip. Over 3 A of current within 10’sof microns of the on-chip mirror, generating ∼ λ .In utilizing this thermal feedback scheme in a cold-atom experiment, attention must be paid to the varyingmagnetic fields produced by the on-chip heating elementthat would perturb the magnetically trapped atoms.While in our prototype, the heater generated 40 mG/mAat a 50 µ m distance, improved designs would reduce this figure to below 1 mG/mA. Moreover, heater wires can be (cid:16)(cid:23)(cid:19)(cid:16)(cid:21)(cid:19)(cid:19) (cid:53) (cid:72) (cid:86) (cid:76) (cid:71)(cid:88)(cid:68) (cid:79) (cid:3) (cid:40) (cid:85)(cid:85) (cid:82) (cid:85) (cid:3) (cid:11) (cid:48) (cid:43) (cid:93) (cid:12) (cid:21)(cid:19)(cid:20)(cid:19)(cid:19) (cid:87)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11)(cid:80)(cid:86)(cid:12) (cid:11)(cid:76)(cid:76)(cid:12)(cid:11)(cid:76)(cid:12) (cid:16)(cid:20)(cid:19)(cid:20) (cid:24)(cid:19) FIG. 4: Deviation of cavity resonance frequency due to cur-rent pulses through the waveguide electromagnets. (i) Usingonly feedback to the PZT actuation of the curved cavity mir-ror, a sudden 0.5 A current pulse displaced the cavity reso-nance by more than the 35 MHz cavity linewidth for over 100ms. (ii) With feedback employing both PZT and fast thermalactuation of the cavity mirrors, the cavity resonance remainedstablized well within even the few MHz linewidth of a veryhigh finesse mode for sudden pulses of 3 A through the elec-tromagnet wires. Inset shows the small residual disturbancefrom the 3 A pulse operated with an alternating current at a frequency farfrom the vibration frequencies of trapped atoms, and alsofrom Larmor precession frequency at the bias field of themagnetic trap. The net effect of the residual oscillatingmagnetic field is to create adiabatic potentials [20, 21] atsub-nanokelvin levels.In conclusion, we have demonstrated the fabricationof magnetic trapping circuitry to be compatible with thedirect integration of micron-scale high reflectivity mir-rors. The thermal coupling between the atom trappingand optical elements has been accounted for and utilizedto rapidly actuate an optical cavity. The scalable mi-crofabrication processes used to create this CQED/atomchip allow for many cavities to be integrated onto a sin-gle atom chip, enhancing the potential of quantum opti-cal and quantum atom optical devices. Furthermore, therapid thermal actuation of low-loss optical componentsdemonstrated in this work may find use in applicationsnot related to atom chip experiments, e.g. those requir-ing high-finesse resonators to be stabilized even in noisyenvironments.We would like to thank Daniel Brooks for assistancein this experiment. This work was supported by theAFOSR under Grant No. FA9550-04-1-0461, and by theDavid and Lucile Packard Foundation. [1] M. Drndic et al., App. Phys. Lett. , 2906 (1998).[2] J. Reichel, W. H¨ansel, and T. H¨ansch, Phys. Rev. Lett. , 3398 (1999).[3] R. Folman et al., Phys. Rev. Lett. , 4749 (2000).[4] H. Ott et al., Phys. Rev. Lett. , 230401 (2001).[5] W. H¨ansel et al., Nature , 498 (2001).[6] T. Steinmetz et al., App. Phys. Lett. , 111110 (2006).[7] P. 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