We explore the feasibility of single atom detection on an atom chip by using a tiny fluorescence detector mounted on the chip. Resonant fluorescence from a trapped ultracold atom will be collected with a miniature aspheric lens and taken out of a vacuum chamber through a fiber. During detection, the atom can be held at the focus of the detector with a dipole trapping beam introduced through the same fiber. We have experimentally determined the optical performance of such a detector, taking into account effects such as stray light from the dipole trapping beam and chromatic aberration. The collection efficiency for isotropically emitted radiation is experimentally obtained to be 2.5%. From this, it is estimated that the fluorescence emitted from a single Rb atom will produce a photon count rate of 4.7×104 Hz, which is much larger than the shot noise limited background fluctuations.
© 2006 Optical Society of America
Atom chips [1, 2] have drastically simplified the generation of atomic Bose-Einstein condensates [3, 4] and provide unparalleled atom manipulation capabilities while maintaining attractively long atomic coherence times . Due to these features, atom chips are promising candidates for neutral-atom quantum information processing [6, 7].
For using individual atoms as qubits, single atom manipulation and observation are required. Recently, a single atom has been trapped with dipole force and observed by fluorescence detection using a high numerical-aperture (NA) lens [8, 9]. In addition, a single atom has been manipulated under strong-coupling conditions in a high-finesse resonator [10, 11]. For integration of atomic qubits, these techniques need to be applied on a microchip, overcoming difficulties associated with the presence of substrate. So far, no experimental results have been reported for single-atom detection on atom chips. For fluorescence detection – conceptually simpler than the absorptive or dispersive detection using a cavity – only some initial ideas are briefly mentioned in the literature [12–14]. In particular, the crucial problem of stray light from the surface (located 100 µm or less from the atom) has not been addressed.
In this letter, we describe a simple, fiber-coupled, miniaturized fluorescence detector, and we present measurements of collection efficiency and stray light intensity in the presence of both excitation and dipole trapping light. From these measurements, we deduce that the detector will indeed be capable of detecting the fluorescence emitted by a single atom trapped above the atom chip. The basic idea is to use a lens of very short focal length, placed very close to the atom. This lens collects a significant fraction of the emitted photons even when the lens diameter is small. Furthermore, the small depth of field, combined with the fiber core acting as an aperture stop, leads to an inherently good rejection of stray light originating elsewhere. The second design choice concerns the trapping mechanism that holds the atom in the focus of the detector. An untrapped atom would quickly diffuse out of detector focus due to the random photon recoil associated with spontaneous emission – too quickly to collect enough photons for detection in spite of the relatively high collection efficiency. Therefore, a trap is needed to hold the atom in the focus of the lens while it scatters photons. It should be possible to use an on-chip magnetic trap for this purpose; however, this requires a specific relative orientation of magnetic field axis, lens optical axis, and excitation beam axis and polarization, which is difficult to realize in practice. An optical dipole trap is less restrictive in this respect because it traps all Zeeman sublevels. Furthermore, if the detection lens and fiber are used to introduce a red-detuned dipole trapping beam, the trap position is automatically aligned with respect to the detector focus. For these reasons, we consider here the case of dipole trap.
Figure 1 schematically shows the setup. The detector is made by inserting both a single mode (not polarization-maintaining) fiber – mounted inside a ferrule – and an aspheric lens (Geltech 350200-B, NA=0.44) into a glass tube with an inner diameter of 1.8 mm. Using an adequately shaped spacer, this subassembly is glued onto the chip such that the detection axis forms an angle of 45 degrees with respect to the surface. The subassembly is about 1 cm high, imposing a distance of the same order between the cold atom production region and the detector to avoid blocking trapping beams if a mirror-MOT [1, 2] is used. The focus of the detector, located about 0.8 mm away from the lens, is aligned so that it coincides with the center of a three-dimensional magnetic trap that will be produced 100 µm above the surface using a current-carrying wire on the chip. 87Rb atoms will be brought to this trap by a magnetic guide [15, 16] or conveyer belt [17, 18]. A dipole trapping laser with a wavelength of 830 nm (red-detuned by 50 nm from the Rb D2 line at 780 nm) is introduced through the fiber, and one or several atoms will be transferred from the magnetic trap to the focus of the 830 nm beam due to the attractive dipole force. For excitation of resonant fluorescence from the atom, two counterpropagating laser beams, directed parallel to the chip surface and perpendicular to the detector axis, and red-detuned by a few linewidths with respect to the |52S1/2,F=2>-|52P3/2,F=3> transition, illuminate the trapping region. In addition to exciting fluorescence, these beams provide one-dimensional cooling of the atom, so that only diffusive heating will remain.
Outside the vacuum chamber, the trapping beam produced by a laser diode with a power of 150 mW is first-order diffracted by a ruled grating with 1200 grooves/mm to remove some weak 780 nm fluorescence that is present in its spectrum. The trapping beam is polarized parallel to the grating lines, and the diffraction efficiency is 74.5 %. Then, after reflection by a dichroic mirror with a reflectance of 98.2%, 65 mW of trapping light are coupled into the single mode fiber with facet A angle-cleaved at 8 degrees. Here, we define the fiber facet at the detector side as facet B and the other as facet A. Furthermore, we take the trapping beam direction as positive and the other as negative. The facet B is cleaved at a right angle so that the trapping beam axis coincides with the fiber axis for simple alignment. This simplicity of alignment comes at the price of a back reflection of the trapping beam in the negative direction from the facet B. In order to remove this reflection, which is superimposed on the fluorescence signal, the signal is diffracted in first order by another ruled grating with 1200 grooves/mm after passing through the dichroic mirror with transmittance of 91.8%. The diffraction efficiency of the grating is 61.8% at random polarization. Next, the beam passes through two interference filters, each having a transmittance of 50% at 780 nm and a FWHM band width of 10 nm, to further suppress 830 nm light. Finally, the signal is coupled into a multimode fiber and detected by an avalanche photodiode (APD) with a quantum efficiency of 0.76.
In order to evaluate the collection efficiency for fluorescence light emitted at the center of the dipole trap, chromatic aberration between 780 nm and 830 nm must be taken into account, since it shifts the dipole trap center out of the detector focus. Figure 2(a) shows an experimental setup for position-dependent spot size measurement to obtain the chromatic aberration of the foci and the Rayleigh lengths, the latter being needed to determine the depth of focus. 780 nm light and 830 nm light are coupled into the same fiber by using a nonpolarizing beamsplitter (NPBS) (only one of the beams is unblocked at a given time). Spot size is obtained by measuring the light power behind a knife edge, which is transversely scanned by a piezo actuator and longitudinally displaced using a piezo near the focus and the micrometer screw of a translation stage far from the focus. The result is fitted with an error function. Spot sizes (half width at 1/e2 of maximum intensity) in the vicinity of the foci are fitted to a function, w(z)=w 0(1+(z-z 0)2/)1/2, where w 0, z, z 0 and z R are the beam waist, longitudinal position, focal position and Rayleigh length, respectively [Fig. 2(b)]. Chromatic aberration is obtained as the difference between the focal positions z 0,780 and z 0,830 of 780 nm light and 830 nm light, i.e., a c=z 0,830-z 0,780.
Figure 2(c) shows the dependence of ac (black squares) and z R of 780 nm light (red circles) on the distance between the lens and the facet B of the fiber, d. For all d, the chromatic aberration is less than the Rayleigh length. The measured chromatic aberration agrees very well with the result produced by a ray tracing program (OSLO), and is also well approximated by the lensmaker’s formula. Both the chromatic aberration and the Rayleigh length decrease with increasing d, becoming almost constant for d≥5 mm. Qualitatively, this is the expected behaviour. However, both the spot size in the focus and the Rayleigh length are significantly larger (up to a factor of 2) than would be expected for the fiber output beam focused by a thin lens. For the larger values of d, some clipping occurs (at d=2.5 mm, the fiber output beam diameter is half the lens aperture diameter); however, this clipping does not explain the observed Rayleigh range . We are currently unable to explain this discrepancy. For the single atom detection task, it is desirable that the chromatic aberration remain much smaller than the Rayleigh length, as is the case here. It should be noted that this is a feature of the particular lens type used in the experiment, and is not necessarily the case for other lenses. Indeed, we measured a chromatic aberration exceeding the Rayleigh length in the case of a GRIN lens (at variance with the OSLO prediction) – and abandoned the GRIN lens for this reason.
It is important to know how much the chromatic aberration reduces the collection efficiency of atomic fluorescence. We experimentally determine an upper bound for this reduction by performing the following measurement: A flat mirror is inserted in front of the aspheric lens, and 830 nm light output from the fiber is retroreflected toward facet B of the fiber. We adjust the mirror position and angle so that the coupling efficiency of retroreflected 830 nm light in the negative direction, i.e η 830=P A,830/P B,830 (P B,λ, P A,λ: the input power on the facet B, the output power from facet A, respectively, where λ indicates the wavelength of light.) is optimized. The optimization of the coupling efficiency should ensure, in particular, that the mirror is in the focal plane of 830 nm beam. Now, we block the 830 nm light beam, and couple the 780 nm light beam into the fiber. Then, we measure the coupling efficiency η 780 of 780 nm light retroreflected by the mirror. To that end, we directly measure the power of the light impinging on the mirror (mirror is temporally taken away) and the back reflection (mirror put back in place) after separation by the NPBS from the incident light. P B,λ and P A,λ are deduced from these light powers, the reflectivity of the mirror, and the separation ratio of the NPBS. By geometric-optical consideration, the retroreflected beam corresponds to that emitted by a source located 2ac away from the 780 nm focus. Atoms in the dipole trap will be located only ac away from this focus, and therefore η 780 is a conservative estimate. Furthermore, this experiment allows us to optimize η 780 as a function of distance d. As shown by the black squares in Fig. 3, the maximum coupling efficiency is 0.59 at d=5 mm. This measured optimum distance is consistent with the fact that the lens is designed for this distance. (This result is not completely trivial, because the 780 nm source is not in the 780 nm focus.)
η 780 is not yet a good estimate of the collection efficiency α for atomic fluorescence, which is the ratio of (the fluorescence power coupled into the fiber) to (the total fluorescence power radiated by the atom). This is because the light retroreflected from the mirror forms a cone, not a dipole emission pattern. In the simplest case of a spherical dipole, α can be estimated from η 780 as α=(Ω/4π) Θ η 780, where Ω is the solid angle of the lens in view from the trapped atom and Θ is the power of fluorescence within the permissible maximal NA=0.12 of the fiber divided by that of fluorescence collected by the lens, respectively. The red circles in Fig. 3 show the estimated collection efficiency α as a function of the distance d. At longer distance d, the solid angle becomes larger since the focus is closer to the lens, and the ratio within the permissible NA of the fiber also increases. Nevertheless, the maximum of the collection efficiency is obtained at d=5 mm and has the value α=0.025. Since we used a conservative estimate for η 780, we thus expect to collect more than 2.5% of the total fluorescence power radiated by a trapped atom.
Due to the finite transmittance and diffraction efficiency of the optics in addition to the quantum efficiency of the APD, the total efficiency, which means the ratio of the photon count rate of the fluorescence detected by the APD to the atom’s photon emission rate, is reduced by another factor ~5 from α=0.025 to an overall efficiency κ=4.9×10-3, which would be comparable to the state of the art of existing, macroscopic fluorescence detectors for single atoms [20, 21]. The estimated single-photon fluorescence count rate is thus γ=Γ/2 s/(1+s) κ=47 kHz at s=1, where Γ/2π=6.1 MHz is the natural linewidth of the rubidium D2 line and s is the saturation parameter.
We now turn to most important point, which is the measurement of the background count rate. Background can be caused not only by the APD itself (“dark counts”), but also by stray light from the 780 nm excitation beams and from the 830 nm trapping beam. In particular, our setup contains the chip surface, not found in other single-atom fluorescence detectors, which is a potential source of stray light. The optical axis of the detector is inclined by 45 degrees with respect to the chip, so that the detector “looks at” the surface, but its small depth of focus (a few µm) compared to its distance from the chip surface (100 µm) should provide a high degree of rejection. Nevertheless, a measurement under realistic conditions is needed to reliably quantify this rejection. We measured the background count rate in a realistic configuration, with the detector mounted on the chip, and both the dipole trapping beam and the counterpropagating excitation beams switched on. The 830 nm laser source, the optics to separate 780 nm light from 830 nm light, and the APD were put on a metallic breadboard and enclosed with a black box made of cardboard to shut the surrounding light out. The chip and the atom detector were outside the box, and the 830 nm trapping beam went out of the box through the fiber. Under these conditions, we found a background rate β~4 kHz. The background counts can be classified into ones by reflection light of the 830 nm trapping beam by the fiber facets, β ref, ones by 830 nm scattered light from the trapping laser source and optics in the box, β 830, ones by 780 nm scattered light around the atom detector induced by the excitation beams, β 780, and dark counts of the APD, β dark. By turning on/off the lasers and by blocking/unblocking the path for the fluorescence, we found that β ref : β 830 : β dark=6 : 5 : 14 in our setup. Thus, in our case, the noise is dominated by the APD dark count rate (2.2 kHz). Note that much better APDs exist with dark count rates as low as 25 Hz, so that this contribution can be reduced to insignificant values. Using such an APD would reduce the total background by more than a factor of 2, leaving β ref and β 830 as the dominant background sources with approximately equal weight. Remarkably, β 780 was negligible, in spite of the relatively high intensity per beam of 8.5 I s, which is chosen to give a saturation parameter s=1 at a detuning of -2Γ. Here, I s=1.6 mW/cm2 is the on-resonance saturation intensity. This confirms that the chip surface is not a serious problem for fluorescence detection.
In a typical atom detection experiment, the detector counts will be accumulated over a given time τ (which should be as short as possible as the excitation light field “heats up” the atom, ultimately ejecting it from the trap). Let us calculate the signal-to-noise ratio of our detector as a function of τ. The total number of counts accumulated, Nc(τ), contains contributions from the atomic fluorescence and from the background. Its average value is N̄c =(γ+β)τ; assuming that both signal and background are shot-noise limited, the noise on this signal is . The mean value of the background can be subtracted, but the remaining useful signal (with a mean value of τγ) still has the full noise on it. The signal-tonoise ratio φ is therefore
A signal-to-noise ratio of 1 is obtained with for τ~23 µs, and a detection time of 210 µs is sufficient to detect a single atom with a signal-to-noise ratio of 3. In this latter case, the detector would count an average number of 9.8 fluorescence plus 0.8 background photons, with shot-noise limited variations of ±3.2 counts.
Finally, let us estimate the heating caused by the random photon recoils during the detection, and compare it to the depth of the dipole trap. At linear polarization, the potential depth of the dipole trap is 
where c, P, ω 0 and Δ i (i=1,2) are the speed of light in vacuum, the beam power, the average over resonant frequencies of D1 and D2 lines, and detuning to the Di (i=1, 2) line, respectively. For our experimental conditions, w 0=2.0 µm, P=65 mW, ω 0/2π=3.8×1014 Hz, Δ 1/2π=-1.6×1013 Hz, Δ 2 /2π=-2.3×1013 Hz, we find U dip/kB =7.0 mK. On the other hand, the heating rate by spontaneous emission is approximately given by R sp=1/3 Γ sp T r , where T r=h 2/(mkB λ2) is the single-photon recoil temperature and Γ sp=Γ/2×s/(1+s) is the photon scattering rate. For s=1, the heating by the excitation beams is obtained as R sp=1.1 mK/ms. We thus obtain an estimate of τ trap ~ U dip/R sp ~ 6.1 ms for the lifetime of the fluorescing atom in the dipole trap, much longer than the required detection time. There is also position diffusion due to the heating, but the mean position remains smaller than w 0 and z R during the detection time, so that the detection efficiency remains essentially constant.
To summarize our results, we found that our simple fluorescence detector, combined with a dipole trap using the same optics and a cheap 830 nm diode, provides a high collection efficiency and ample storage time for detection with a good signal-to-noise ratio. Some care must be taken to filter out stray light from the 830 nm trapping beam; remarkably, however, the excitation beams do not cause significant background in spite of the nearby chip surface. These results also suggest that crosstalk should be very weak when multiple detectors are densely spaced side-by-side, providing favorable conditions for scaling up to parallel multiqubit detection. Techniques such as V-groove alignement, developed for telecom devices, provide a well-developed technological framework for this task. From the compactness and the facility of the alignment on the chip, we expect this detector to be a useful tool for singleatom observation on atom chips. Demonstration of single-atom detection with this detector was delayed by A. T.’s move back to Japan, but we expect to perform such an experiment on a timescale of less than a year. The detector itself can be further improved to realize a shorter detection time and/or still simpler design. Note that the expected fluorescence count rate is an order of magnitude higher than the background rate. In such a case, the detection time τ is dominated by the requirement to accumulate a nonzero number of fluorescence photons with high probability. This means that, to first approximation, τ is inversely proportional to the total efficiency κ, whereas further reduction of the background rate β only marginally reduces τ. To improve κ, there are two ways: the NA of the lens may still be somewhat increased (although this may aggravate the chromatic aberration problem), and the losses in the optical system can be reduced. The shorter the detection time, the more the intensity of the dipole trap may be reduced (which in turn allows less elaborate filtering, i.e. reduced attenuation), and it becomes interesting to consider whether in such an improved detector, detection can be realized without any dipole trap at all.
This work was supported in part by the EU’s IST program (ACQP, IST-2001-38863), by the CONQUEST Research Training Network (MRTN-CT-2003-505089), and by the Kompetenznetzwerk Quanteninformationsverarbeitung of the Bavarian State Government. A. T. thanks the Japan Society for the Promotion of Science for his stipend.
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