Stable fiber-based Fabry-Pérot cavity
ABSTRACT The development of a fiber-based, tunable optical cavity with open access is reported. The cavity is of the Fabry-Pérot type and is formed with miniature spherical mirrors positioned on the end of single- or multimode optical fibers by a transfer technique, which involves lifting a high-quality mirror from a smooth convex substrate, either a ball lens or microlens. The cavities typically have a finesse of ∼1000 and a mode volume of 600 μ m 3 . The detection of small ensembles of cold Rb atoms guided through such a cavity on an atom chip is demonstrated.
arXiv:physics/0606231v1 [physics.atom-ph] 27 Jun 2006
A stable fiber-based Fabry-Perot cavity
T. Steinmetz,1A. Balocchi,2Y. Colombe,1D. Hunger,1
T. W. H¨ ansch,1R. J. Warburton,2and J. Reichel3
1Department f¨ ur Physik, Ludwig-Maximilians-Universit¨ at,
Schellingstrasse 4/III, 80799 M¨ unchen, Germany
2School of Engineering and Physical Sciences,
Heriot-Watt University, Edinburgh EH14 4AS, UK
3Laboratoire Kastler Brossel de l’E.N.S.,
24 rue Lhomond, 75231 Paris Cedex 05, France
(Dated: February 2, 2008)
We report the development of a fiber-based, tunable optical cavity with open access. The cavity is of
the Fabry-Perot type and is formed with miniature spherical mirrors positioned on the end of single- or
multi-mode optical fibers by a transfer technique which involves lifting a high-quality mirror from a smooth
convex substrate, either a ball lens or micro-lens. The cavities typically have a finesse of ∼ 1,000 and
a mode volume of 600µm3. We demonstrate the detection of small ensembles of cold Rb atoms guided
through such a cavity on an atom chip.
An optical cavity amplifies the interaction between light and matter by recirculation of the
light at a resonant frequency. This feature is exploited in a number of fields, notably lasers and
optical sensors. Furthermore, it is crucial to experiments and possible technologies based on
exploiting the quantum mechanical properties of individual atoms and photons. In this field of
cavity quantum electrodynamics (CQED), the crucial features of the cavity are a small mode waist
and/or mode volume Vm, and a high finesse F = ∆ν/δν (where ∆ν is the free spectral range and
δν the linewidth of the cavity), equivalently a high Q factor Q = ν/δν . The “gold standard”
for CQED cavities is still being set by macroscopic Fabry-Perot (FP) cavities with superpolished,
concave mirrors. These mirrors have relatively large radii of curvature (R = 20cm is typical)
and achieve record finesse values of F > 2 × 106. However, there are situations where
cavities of this type cannot be used, and a number of alternative cavity designs have been proposed
(see for example ). A notable example calling for an alternative cavity design is single-atom
detection for quantum information processing on atom chips [4, 5, 6, 7] where the macroscopic
cavity is incompatible with the microscopic chip. Another example concerns the insertion of
quantum objects such as quantum dots and molecules into cavities where the need for cryogenic
temperatures makes a macroscopic design problematic. While microscopic cavities are being
actively developed, existing designs typically lack an easy way of tuning the cavity into resonance.
An optical fiber-based resonator offers an attractive way forward [7, 8]. Here we describe
a fiber-coupled Fabry-Perot (FFP) cavity that employs concave dielectric mirror coatings with
small radius of curvature, realized on the fiber tip. A stable cavity is constructed as shown in
Fig. 1(a),(b), either from one such fiber tip facing a planar mirror (“1FFP”), or from two closely
spaced fiber tips placed face-to-face (“2FFP”). Thus, unlike the design of , the cavity can easily
We demonstrate how such cavities can be easily fabricated using commercially available lift-off
coatings. Tunability is achieved by attaching one of the fibers to a piezoelectric actuator. Because
of the small fiber diameter (125µm), very short cavities (< 10λ/2) can be realized even with
radii of curvature R ≤ 1mm, still leaving a sufficiently large gap to introduce cold atoms. We
achieve stable cavity modes with a finesse of ∼ 1,000 in the near infrared. The mode volume is
Vm= 600µm3, to be compared to Vm= 1680µm3for the smallest-volumemacroscopic FP cavity
that has been used with atoms . In terms of CQED parameters, the small mode volume results
in an exceptionally high coherent atom-photon coupling rate, g0/2π = 180MHz (calculated for
the Rb D2 line at λ = 780nm) . Therefore, in spite of the comparatively high damping rate,
κ/2π = 2.65GHz which results from the moderate finesse and short length, the cavity reaches a
single-atom cooperativity parameter greater than unity, C = g2
0/2κγ = 2.1 where γ/2π = 3MHz
is the atomic linewidth, signaling the onset of quantum effects such as enhanced spontaneous
emissionintothecavity modeand asignificant modificationof cavitytransmissionby thepresence
of a single atom. The potential of this approach is demonstrated here with an experiment using
a 2FFP cavity to detect an extremely weak flux of cold atoms magnetically guided on an atom
chip. We present this technology not only as an important stepping stone towards on-chip single
atom detection but also for cavity experiments with quantum dots, semiconductor nanocrystals
and molecules, and for telecoms devices.
The concave mirrors are fabricated from a convex template and a lift-off step. For large radii of
curvature, ≥ 500 µm, the template is a commercial ball lens whereas for smaller radii, 100 − 500
µm, thetemplateisasilicamicro-lensspeciallyfabricated fortheseexperiments. Themicro-lenses
are etched into a planar silica substrate following the melting and re-solidification of a photoresist
mesa. Surface tension provides an extremely smooth photoresist surface such that the roughness
in the micro-lens is determined only by the subsequent dry-etching step and can be as small as ∼ 1
nm. The template is coated  in one run with a release layer and silica-titania dielectric Bragg
stack, with a stopband centered either at 780 nm or 850 nm and nominal reflectivity of 99.7%.
We then position a cleaved single mode fiber immediately above the center of the coated lens by
maximizing the back reflection of a laser beam coupled into the fiber. The fiber is then glued in
place with an UV-curing epoxy, after which the application of a small force is sufficient to detach
the mirror from the original substrate. The result is a fiber functionalized with a highly reflecting
concave mirror, as shown in Fig. 1(c). A complete 2FFP cavity is shown in Fig. 1(d).
In order to characterize the modes of a 1FFP cavity, we measured the white light transmission
spectrum for several values of the cavity length L. We find that stable cavity modes with high F
can be established with little attention to the alignment, unlike the planar-planar cavity geometry
which isextremelysensitivetoalignmentand mechanical noise. Theresultsare showninFig. 2(a).
As expected for a FP cavity, for each L there is a series of longitudinal modes, until at the smallest
L there is just one longitudinal mode in the stopband. Each longitudinal mode consists of a
series of finely spaced modes, corresponding to the different transverse modes. This lifting of the
degeneracy of the transverse modes allows a spectroscopic determination of the mirror curvature.
Fig. 2(b) plots the wavelength shift of the higher order modes relative to the fundamental as a
function of L showing how the spacing increases as L decreases. The solid curves in Fig. 2 are
FIG. 1: (a) and (b) Concept of the miniature cavity. The basic building block is an optical fiber functional-
ized with a concave dielectric mirror. Two such fibers, brought sufficiently close to each other, result in a
stable Fabry-Perot cavity which can be interrogated remotely, either in transmission or in reflection, through
the two fibers (“2FFP” configuration, (a)). Alternatively, a single fiber can be brought close to a reflecting
planar surface (“1FFP” configuration, (b)). The 1FFP configuration is suitable for use with nanofabricated
structures such as quantum dots. (c) A single-mode optical fiber, total diameter 125 µm processed with a
concave mirror. The mirror has radius 1000 µm with a stopband centered at 780 nm. (d) A miniature cavity,
realizing the configuration (a), mounted on an atom chip used in the detection of cold atoms (Fig. 4).
the results from Gaussian optics for a stable, planar-spherical cavity , ∆λ = (λ2/2πL)∆(m+
n)cos−1?1 − L/R where m, n are the lateral mode indices. At large (small) L, the results
are best described with a radius of about 200 (230) µm. This compares well with the radius of
the micro-lens template, 250 µm. The slight dependence on L is likely to result from a slight
“softening” of the mirror away from its center: as L increases, the beam waist at the curved mirror
increases, probing more of the curved mirror.
The limited resolution of the spectrometer prohibits a proper measurement of the finesse, and
only a lower limit can be deduced (F > 500 for small L). We have therefore measured the
cavity transmission as a function of L using grating-stabilized diode lasers (Fig. 3). To determine
the finesse, two lasers were simultaneously coupled into the cavity. The first laser is locked to
a sub-Doppler line in the87Rb D2 spectrum at λ = 780.27nm, the second is tuned several κ
away to 780.6nm using a wavemeter. The known wavelength difference of the two lasers allows
us to calibrate the length scan with a better precision than the length-voltage characteristics of
the piezo. Additionally, we simultaneously recorded the transmission of a third diode laser at
FIG. 2: (a) White light transmission spectra of a 1FFP cavity recorded at three different cavity lengths,
L. The mirrors have a stopband centered at 850 nm. L is the effective cavity length, determined by L =
1/2∆(1/λ) where ∆(1/λ) is the change in wave number from one fundamental longitudinal mode to the
next. The modes are labeled with the sum of the two lateral mode indices, m and n. The widths of
the transmission peaks are limited by the spectrometer and therefore do not reflect the true finesse. (b)
Separation in wavelength of the higher lateral modes from the fundamental mode as a function of L at
λ = 850 nm. The solid (dashed) line represents the analytical result for a spherical-planar FP cavity with
radius R = 230 (200) µm.
828.25nm in order to determine unambiguously the absolute cavity length. As a typical result, we
have measured a finesse F = 1,050 for a 2FFP cavity with L = 27µm and R = 1,000µm using
a single-mode fiber on the input side and a multimode fiber on the output side. This is in good
agreement with independent measurements of the mirror transmission, T = 8 × 10−4, and loss,
ℓ = 2.4 × 10−3. From these values, the expected finesse is F = π/(T + ℓ) = 980 ± 40. This
indicates that the finesse of the FFP is as high as the coatings allow. The 1/e beam waist in the
cavity in Fig. 3 is w = 5.4µm, implying a cavity mode volume Vm∼ 600 µm3and C = 2.1 for
We have used the 2FFP cavity as a very sensitive detector for magnetically guided atoms on an
atom chip. The experimental setup is similar to our previous experiments [11, 12], but contains
Effective cavity length (µm)?
Transmission (arb. units)?
Relative length (nm)?
FIG. 3: Transmission of a 2FFP cavity versus cavity length. A piezo is used to vary the cavity length. The
absolute length is determined by using up to three lasers as described in the text. The mirrors have radius
1,000 µm with a stopband centered at 780 nm. The cavity has an effective cavity length of 27µm with a
finesse of 1050; equivalently, free spectral range 5500 GHz and mode width (FWHM) 5.29 GHz. The inset
shows the line shape of the fundamental (0,0) mode.
an FFP subassembly. Each fiber is glued onto a piezoelectric actuator, and the piezos are glued
onto a ceramic bridge while monitoring the cavity transmission signal. The mirror spacing on
axis is 27µm as in Fig. 3, leading to a gap between mirror edges of ∼ 15µm; the finesse is 260.
The subassembly is glued onto the chip with a 230µm separation between the cavity axis and the
chip surface (Fig. 4 (a)). A magnetically trapped cloud of87Rb atoms at a temperature of 70µK is
produced in an initial trap and then released into a very elongated Ioffe-Pritchard potential, created
using a “Z wire” . This potential guides the atoms through the center of the resonator mode.
The cavity mode is excited by a very weak resonant probe laser, both the laser and the mode being
tuned to atomic resonance. The transmitted signal is detected with a photon counter. Fig. 4 (b)
shows sample transmission signals with and without atoms. We have independently determined
the atomic density and temperature before entry into the cavity using absorption imaging and
time-of-flight analysis. Integrating the initial density over the cavity mode yields an upper-bound
estimate Nmaxfor the number of atoms in the cavity mode, Nmax∼ 50. It is clear however that
the true number of atoms contributing to the signal is much lower because the transverse size of
the atom cloud is significantly larger than the gap between the mirrors, so that a large part of the
0 10 20 30 40 50 60 70 80 90 100
(counts / 500µs)
FIG. 4: Atom detection with an on-chip fiber resonator. (a) At t = 0, a magnetically trapped atom cloud
(T = 70µK) is released into a very elongated Ioffe-Pritchard potential, created using the wire shown in
gray. This potential guides the atoms through the center of the resonator mode. (b) Transmission signal of
the fiber resonator for a single experimental run (solid line), along with an empty cavity transmission signal
(dashed line). The transmission drops to 35% of the empty-resonator value.
atoms is lost upon entering the cavity, and does not contribute to the signal.
Our current cavities aim for high cooperativity. It is interesting however to consider what
improvements would be necessary to enter the strong coupling regime of CQED, i.e., g0> κ,γ
. To obtain strong coupling, it is preferable to increase the mirror distance L provided L ≪ R:
for a given R, κ drops as κ ∝ L−1, whereas g0only decreases as g0 ∝ L−3/4. L = 200µm
is a realistic value where alignment should still be manageable, and where the spot size on the
mirrors remains much smaller than the mirror diameter, so that clipping loss can still be neglected.
At this L, the parameters of the 2FFP cavity with R = 1mm would become g0/2π = 42MHz
and κ/2π = 360MHz. Thus, the finesse needs to be improved by roughly a factor of 10, to
F = 10,000, in order to reach the strong coupling regime. Presently, the finesse of our cavities
is limited by the quality of the multilayer coatings. However, the transfer coating technology
continues to improveas suggested by the fact that the transfer coatings used in , fabricated after
the ones used here, resulted in a measured finesse F = 6,000. Speculating that the coating quality
can be improved further, the remaining issue is the surface roughness of the template for the liftoff
process. For a ball lens from the batch used in our current cavities, an AFM measurement gave an
rms roughness of σ = 1.7nm. Following a standard estimate for scattering loss, S = (4πσ/λ)2,
this roughness must be improved to σ ≤ 0.7nm which is achievable both with superpolishing and
with micro-lens fabrication.
We conclude by noting that, even without any further improvement, the FFP cavities described
here shouldenable single-atomdetectivitywith good signal-to-noiseratio [6, 7]. Unlikedispersive
detection withouta resonator, this techniquewill ultimatelyallow detection with less than one
spontaneous emission per atom on average, enabling preparation of single-atom states.
A.B. and R.J.W. acknowledgefinancial support fromEPSRC (UK)and theRoyal Society (Lon-
don). The remaining authors acknowledge support from the EU (project IST-2001-38863, ACQP)
and from the Bavarian State Government (Kompetenznetzwerk Quanteninformation – A8). Y.C.
thanks the EU CONQUEST network (MRTN-CT-2003-505089) for his stipend.
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