Nano-structured alkali-metal vapor cells

Atom-light interactions in nano-scale systems hold great promise for novel technologies based on integrated emitters and optical modes. We present the design architecture, construction method, and characterization of an all-glass alkali-metal vapor cell with nanometer-scale internal structure. Our cell has a glue-free design which allows versatile optical access, in particular with high numerical aperture optics. By performing spectroscopy in different illumination and detection schemes, we investigate atomic densities and velocity distributions in various nanoscopic landscapes. We apply a two-photon excitation scheme to atoms confined in one dimension within our cells, achieving a resonance line-width of 32 MHz in a counter-propagating geometry, and 57.5 MHz in a co-propagating geometry. Both of these are considerably narrower than the Doppler width ($\sim$ GHz), and are limited by transit time broadening and velocity selection. We also demonstrate sub-Doppler line-widths for atoms confined in two dimensions to micron-sized channels. Furthermore, we illustrate control over vapor density within our cells through nano-scale confinement alone, which could offer a scalable route towards room-temperature devices with single atoms within an interaction volume. Our design offers a robust platform for miniaturized devices that could easily be combined with integrated photonic circuits.

Miniaturization of thermal vapors is an emerging alternative approach to atomic physics at the nanometerscale. Examples include confinement of vapors to micronsized hollow core fibers [48], construction of sub-micron alkali-metal vapor cells [35,[49][50][51][52], as well as implementation of waveguides [53][54][55][56][57], diffractive elements [58], and opto-mechanical features [59]. However, much work remains ahead before nanoscopic vapor-based devices can be used in technological applications, e.g. for local sensing [15] or quantum networks [39,60]. In particular, reliable fabrication methods are needed for the realization of scalable and efficient platforms. Furthermore, the inter-actions of the atoms with the cell walls [21,32,33,44,61] as well as their velocity distribution and diffusion behavior have to be investigated and understood.
In this work we present a new platform that produces long lifetime (at least 1 year) alkali-metal vapor nanocells. Using laser lithography and reactive ion etching we create regions with internal dimensions from 2 µm to 400 nm (smaller structures with dimension below 100 nm are possible), filled with rubidium vapor. We demonstrate full optical access that facilitates the use of conventional high numerical aperture (NA) optics for efficient atom-light coupling. We also demonstrate two excitation and detection schemes for atoms confined within various nano-scale structures. Our approach opens doors to efficient and compact architectures for performing quantum nano-optical studies. Figure 1(a) displays the schematics of our glass nanocells, depicting a side view of the cell region, with nanoscopic features located at positions (iii) and (iv). A tube conduit (diameter 5 mm, labelled (vi)) connects this nano-structured region to an alkali-metal reservoir. The glass cell is assembled from three distinct parts that we refer to as: the cover slide (labelled (i)); the block (labelled (ii)); and the reservoir (located below label (vi)). In this work, the block was a fused silica cuboid of dimensions 10 mm×20 mm×30 mm, though this was chosen for manufacturing convenience and could be considerably reduced in size for future applications. The cover slide is a fused silica panel of dimensions 0.5 mm × 20 mm × 30 mm front-facing photograph of the nano-cell. The etched cover slide (i) is contacted onto the block (ii) such that the etched patterns form a nano-thickness region (iii) and nano-channels (iv) between the two glass pieces. An optical contact bond (v) surrounds the etched area to act as a vacuum seal. The rubidium reservoir below (vi) is attached to provide atomic vapor into the nano-structured region. This cell contains areas with confinement in both one and two dimensions. (c) Front-facing bright field microscopy images of various channel structures, with widths 400−5000 nm. A number of copies of these structures are etched into the cover slide to provide a range of depths (400 − 2000 nm). These channel structures reside in the horizontal black bars, labelled (iv) in (b). Vapor is supplied from below in this image. (d) SEM image of a single channel aperture (indicated by the white box in (c)).

II. NANO-CELL FABRICATION
into which we "write" the nano-structures of choice.
To do this, we pattern micro-and nano-scale features into photoresist using direct-write laser lithography, and transfer these to the glass substrate using reactive ion etching [62]. Figure 1(b) shows a photograph of the cell under white-light illumination (full details of cell characterization will be discussed in Section III). The block is optically polished on all sides to increase optical access to the nanoscopic regions, and to facilitate the formation of an optical contact bond (OCB). We form an OCB between the cover slide and the block to act as a vacuum seal encircling the patterned area. The cover slide is placed on the block such that the microand nano-patterns form a confined region between the two pieces, which also overlaps the internal tube of the block to allow vapor to enter. Figure 1(b) shows the OCB surrounding the patterned area, seen as lack of Newton's fringes between the two fused silica pieces. Once an OCB encircling the nano-regions and milled aperture has been formed, the bond is made permanent by firing in a kiln at 1000 • C for 6 h at atmospheric pressure. The OCB process up until firing is reversible. Two fused silica spacer columns (labelled in Fig. 2(a)) were included in our cell design to prevent the cavity thickness from deviating from the design specification due to bowing during the next fabrication step, when the air is pumped out to produce a vacuum.
To load the nano-cell with alkali-metal atoms (in our case rubidium) the fired pieces are attached to a borosilicate glass manifold by glassblowing. A vacuum pump and a rubidium break seal ampoule are attached to the manifold, which is evacuated and sealed. The rubidium ampoule is broken and, by melting with a low flame, liquid rubidium is made to flow towards the block. A short (typically 5 cm) section of the manifold immediately adjacent to the block, and containing condensed rubidium, is then sealed and detached to enclose the complete nanocell. This section of borosilicate glass tube attached to the bottom of the block is referred to as the reservoir (see Fig. 1(a), part (vi)).
We find that our glue-free design is very robust, and we have produced numerous nano-cells with an operation lifetime of over 1 yr. The cells can withstand dozens of heating and cooling cycles between room temperature and 180 • C. In typical operation both the cell block and the reservoir are independently heated, so as to maintain a thermal gradient between the two and thus avoid rubidium condensation in the nano-structured regions. Heating is achieved via patches of sputtered indium tin oxide (ITO) on external surfaces of the cell, which act as resistive heaters when an electric current is applied (not shown in Fig. 1(b)). Experiments with thermal vapors often rely on bulky ovens for cell heating, but the compactness and transparency of our ITO layer allows heating of the cell without compromising optical access or the experimental footprint.
To populate the nano-scale regions with atoms, we find that it is favourable to periodically 'flood' these areas with liquid rubidium by inducing a reverse temperature gradient (reservoir hotter than the nano-region), and then returning to a conventional temperature gradient to evacuate the nano-regions again. After such a cycle small deposits of rubidium remain on the inner surfaces which act as local reservoirs. Figure 1(b) shows a completed nano-cell with the patterned regions made visible by white light interference in the void formed between the two fused silica pieces, producing strong colours. More subtle, however, is the fact that the colors change both gradually and in discrete steps across the patterned area of the nano-cell. The discrete color changes occur by design due to the discrete depth changes selected when patterning the cover slide. The gradual color changes are a result of the surface of the block and the internal surface of the cover slide being non-parallel. We also note that the gradients generally differ before and after the kiln firing process, suggesting the process induces changes in mechanical stress in the two fused silica pieces.

III. CHARACTERIZATION
To characterize the cells, the thickness of the patterned regions is measured after the assembly is complete. To do so, we exploit the fact that the nano-thickness region acts as a low finesse Fabry-Pérot cavity, with the internal surfaces of the fused silica cavity acting as low reflectivity mirrors. The transmission, T , of a Fabry-Pérot interferometer is [63] where R is the reflectivity at the fused silica interface, and δ = 4πl/λ is the phase shift of each subsequent roundtrip reflection in the cavity, with l the cavity length and λ the wavelength of the probing light. The free spectral range of our micro-cavities is of order λ, hence we use white light to span multiple Fabry-Pérot transmission peaks, which are fitted with a model using equation 1 (see Appendix A for further detail). Figure 2(b) shows the result of a horizontal sweep across the face of the nano-cell, with white light spectra taken at 0.1 mm intervals along the axis marked (dashed white line) in Fig. 2(a). This method gives high precision measurements of cavity thickness at each point (with errorbars of order 1 nm). From left to right, we find mean values of 2070 nm, 1020 nm and 420 nm for the discrete thickness regions. The deviation from these mean values, shown in panel (c), reveals a gradual thickness change across the cell. The variations within each thickness region are of the order of 1 %, and show that the nano-cell is slightly concave, which is likely an effect of inhomogeneous reactive ion etching.

IV. DETECTION SCHEMES
The energy levels of rubidium relevant to the detection methods used in this work are shown in Fig. 3. In the most straightforward scheme, a single tunable laser at λ = 780 nm is used to excite Rb atoms from their ground state 5S 1/2 to the excited state 5P 3/2 , i.e. on the D2 line. Extinction spectroscopy in transmission on this (or the D1 line, not shown in Fig. 3) has been the most widely adopted detection technique for studying thermal vapors due to the simplicity of implementation. However, when the optical depth of the system is decreased, as in the case of a nano-thickness vapor, it becomes more challenging to detect the extinction signal due to reduced signal-tonoise [66]. Our geometry allows us to instead perform fluorescence measurements efficiently, employing a high-NA objective lens to collect atomic fluorescence through the cover glass. Two fluorescence detection schemes are used in this work. The single-photon scheme labelled (a) in Fig. 3 allows for detection of fluorescence activity with the excitation laser light spatially filtered from the atomic fluorescence, for example in a total internal reflection fluorescence (TIRF) geometry (see Fig. 4). Alternatively, a two-photon excitation scheme can be used. A 776 nm laser is added to drive population to the 5D 5/2 state, from which there is approximately 7.5 % probability that an atom will decay via the 6P 3/2 state and produce a 420 nm photon [13] (labelled (b) in Fig. 3). This light can be spectrally separated from scattered excitation laser light, providing an even higher signal-to-background ratio than in the single-photon scheme.
Below we discuss the two detection schemes in more detail, and employ them to record spectroscopic data from atoms confined to the nano-cell. In all cases the frequency axis was calibrated by a reference Rb cell in a methodology similar to that performed in reference [67], where the zero of detuning is chosen to be the weighted [64] τ = 246 ns [65] 6.8, 3.0 GHz FIG. 3. Partial rubidium energy level diagram showing key transitions and detunings used to probe the atoms inside the nano-cell in this work. Relevant hyperfine states are indicated for 87 Rb, 85 Rb (note that these are omitted for 6P 3/2 which we do not spectroscopically probe). Two detection schemes used in this work are labelled (a) and (b). Scheme (a) relies on a single excitation laser at 780 nm addressing the rubidium D2 line, driving population to the 5P 3/2 state which then decays via emission of a photon of the same frequency. Scheme (b) employs two lasers at 780 nm and 776 nm to drive atoms to the 5D 5/2 state, from which they can decay via the 6P 3/2 state and produce a photon at 420 nm. The lifetimes of each of these states, τ , are indicated.
line-center of the rubidium D2 transition.

A. Total Internal Reflection Fluorescence (TIRF)
A schematic of the TIRF setup is shown in Fig. 4. Total internal reflection occurs at the glass-vapor interface, and a single-color evanescent light field is created that can drive atomic excitation and induce fluorescence. Although strictly 3-dimensional, we consider only the variation of the laser field along the axial distance z from the interface between the fused silica wall and the vapor. Hence, the evanescent field has the general form E(z) = E 0 e −z/d , where E 0 is the electric field at the boundary immediately outside of the medium in which the total internal reflection is occurring, z is the perpendicular distance from the fused silica wall into the vapor, and d is the evanescent field decay length. This is given by [68]: with n 1 the refractive index of fused silica (≈ 1.45), n 2 the refractive index of the vapor (nominally taken as 1), θ the incident angle, and λ the vacuum wavelength of the light field (we probe the D2 line at λ = 780 nm). Typically we have d ∼ λ/2π, and thus expect frustrated A coupling prism is used to deliver a 780 nm probe beam into the nano-cell, at an angle θ to the normal. When incident on the back interface between the nano-region and the glass, the beam totally internally reflects and an evanescent field is formed inside the nano-region. This field excites the atomic vapor. Fluorescence is collected through the front face of the cell via a f = 2 mm focal length, NA = 0.7 plan apochromat objective lens, onto a single-photon avalanche diode.
total internal reflection to have little effect in our nanocells with have internal dimensions ∼ λ.
To demonstrate the TIRF methodology, experiments were performed to study the transit-time broadening induced by varying evanescent field decay lengths. The nano-cell was heated to 100°C, and fluorescence counts were collected for 10 s with a probe beam power of 10 µW. The resulting fluorescence spectra shown in Fig. 5 contain transitions from each of the two hyperfine 5S 1/2 ground states, for each of the two naturally occurring rubidium isotopes, to the 5P 3/2 state (see Fig. 3) [67]. The hyperfine structure of the 5P 3/2 state, with features ∼ 100 MHz, is not resolved due to Doppler broadening.
To analyze the observed spectra, we consider a lineshape model made by the summing of four Voigt profiles, each centered on one of the four hyperfine ground states observed in the fluorescence spectrum. The full width at half maximum (FWHM) of one Voigt profile is plotted as a function of θ (colored dots, Fig. 5(c)). The trend reveals that the spectra become broader as the incident beam angle is increased. We understand this to be a transit-time broadening caused by the reduced characteristic decay length, d, of the evanescent light field that probes the atoms (see Fig. 5(c) inset).
To examine the observed line-width behavior further, we performed a Monte Carlo simulation. The simulation initializes 3000 individual atoms with a random velocity vector v = v xx + v yŷ + v zẑ (see Fig. 4 for axes definition) such that the distribution of velocity vectors approximates the Maxwell-Boltzmann distribution as expected for an ideal thermal vapor. The spectrum of the ensemble is made up of Lorentzian line-shapes contributed by individual atoms, which are modified in two ways. First, the line-center is shifted by the Doppler effect k · v = kv z as the atom moves with respect to the laboratory frame. Second, the width of the Lorentzian is modified by the short transit time t trans = d/v z across the short decay length d of the evanescent field along z. To put this timescale in perspective, we note that at a typical temperature of 100°C a thermal atom has a mean speed of 330 m s −1 , corresponding to t trans = 0.3 ns across a distance d = 100 nm. We define an effective line-width Γ eff per atom using: where Γ nat is the natural line-width, and α is a unitless factor that attenuates the transit-time broadening. We do not consider atomic interactions or collisions, as typically we have atomic densities of order 10 12 cm −3 and do not have buffer gas within our cells. The 3000 atom simulation was repeated ten times at a number of discrete values of incident beam angle θ to return a mean and standard error for each. A fit to the simulated data is plotted as the black dashed line in Fig. 5(c). We find that with α = 0.3 the simulation captures the experimentally observed trend, however clearly some systematic error exists. For comparison, for transit-time broadening of atoms traversing a Gaussian laser beam the comparable factor is α ≈ 0.2 [69]. More complex modelling is beyond the scope of this work, however, we speculate that the differences between observation and theory come about due to the evanescent field gradient experienced by the atoms, as well as the reduced probability of a fast moving atom being excited by the laser field. Neither of these effects were included in our model. The latter means that atoms with a low transit time are less likely to contribute to the fluorescence signal, reducing the overall broadening effect.

B. Two-Photon Fluorescence Microscopy (TPFM)
As illustrated in the previous section, the technique of single-photon TIRF gives a high signal-to-background ratio for spectroscopy. However, it relies on detection of fluorescence photons at the same frequency as the input laser photons, so although it is theoretically a dark-field method, it is in practice not free of background scattering. This poses a problem in particular for cells with more complex structures such as one-dimensional nanochannels (see, for example, Fig. 1(c)), where laser light is efficiently scattered by the edges. In this section, we detail a two-photon excitation scheme which allows fluorescence detection at 420 nm. The scheme is depicted in Fig. 3, with the fluorescence pathway used for detection labelled (b). This scheme allows for straightforward filtering of any excitation photons scattered by the substrate, using commercially available bandpass filters.
Our nano-cell design allows for the use of high-NA optics, which allows us to optically resolve nano-scale structures, as well as address and collect fluorescence from atoms within individual structures. In fact, in this section we employ a NA = 0.7 plan apochromat microscope objective to address atoms within volumes ∼ λ 3 confined in nano-scale structures, where spatial confinement is typically ≤ 1 µm in one or two dimensions. Figure 6 shows the experimental setup, where the two excitation lasers are delivered to the nano-regions in co-or counterpropagating arrangements, and atomic fluorescence photons are collected via the microscope objective.
The use of two beams leads to atoms experiencing a Doppler shift of the form ∆ν D = (k 1 + k 2 ) · v, where k 1 and k 2 are the wavevectors associated with each beam, and v is the atomic velocity. This, in combination with the velocity distribution of the atomic vapor, leads to resonances being Doppler broadened. In thermal vapor physics it is common to use a counter-propagating geometry with two beams of the same or similar frequencies (|k 1 | ∼ |k 2 |) to resolve sub-Doppler spectral features [67] for use as reference spectra (e.g. the top panel of Fig. 8).
However, for co-propagating beams the summing of the wavevectors generally causes significant Doppler broadening (∼ GHz for the wavelengths used in this study). In this section we will first demonstrate sub-Doppler spectral features from atoms within our nano-cell using a conventional counter-propagating geometry. We will then show that, due to nano-scale confinement induced velocity selection, in a co-propagating geometry our nano-cell also freely allows sub-Doppler features to be observed. In these experiments, we will scan a 780 nm laser through the D2 resonance while employing excited-state polarization spectroscopy [70] to frequency stabilize a second laser at 776 nm to the 5P 3/2 → 5D 5/2 transition. As such we can spectrally resolve the D2 transition through detecting fluorescence photons from the 6P 3/2 → 5S 1/2 transition (see Fig. 3). Firstly we report on the results of implementing a TPFM scheme in which the two excitation beams are counter-propagating in the nano-cell (see (b) in Fig. 6). As can be seen in Fig. 7, this scheme gives well resolved sub-Doppler fluorescence resonances corresponding to the transitions from the hyperfine 5S 1/2 ground states to the allowed 5P 3/2 hyperfine states. Our empirical fit gave a Voigt FWHM of (32 ± 1) MHz, consistent with transit-time broadening with 1 µm confinement. Due to the nature of the two-photon scheme, and 780 nm Detuning, ∆780/(2π) (GHz) A counter-propagating two-photon excitation geometry is used (see inset diagram illustrating atomic layer and input beams, as well as Fig. 6). Note that this spectrum corresponds to the left half of that shown in Fig. 5(a). An empirical fit comprising six Voigt profiles (black dashed) was performed, with the locations of the resonances constrained to the relevant hyperfine transition frequencies, their magnitudes constrained to the isotopic abundance-weighted transition strengths, and their widths set to be equal (but allowed to vary as a fit parameter). This yields a line-width of (32 ± 1) MHz. Partial energy level diagrams are shown above for reference. For this dataset, powers of 350 µW at 780 nm (focussed with the f = 100 mm lens) and 20 µW at 776 nm (focussed with the f = 2 mm lens) were used, with a cell temperature of 60 • C and an integration time of 12 h.
in contrast to single laser pump-probe schemes, crossover resonances are absent. This affords better resolution of the allowed hyperfine transitions.
Spectra were also obtained using the TPFM method with a co-propagating geometry, and a selection of these are shown in Fig. 8. Here the nano-cell was displaced along the optical axis of the microscope objective, such that atoms sampled the laser intensity profile locally. The spectral features in the datasets arise due to the hyperfine structure of the 5P 3/2 state, though not all hyperfine states are fully observed or resolved. We do not observe the same activity ratios between hyperfine levels as in counter-propagating case (Fig 7), but we speculate this is to do with the transition the 776 nm laser is Reference spectrum produced using a pumpprobe setup in a 75 mm cell. Each Doppler-broadened profile exhibits six sub-Doppler features (some too weak to be seen), with the three indicated corresponding to the hyperfine 5P 3/2 states (see Fig. 7), and the other three to crossover resonances between these. Below: TPFM spectra recorded with 780 nm and 776 nm beams co-propagating (both along path (a) in Fig. 6) incident on a region of the nano-cell with 1 µm depth in the direction of the excitation beams. The nano-cell was translated with respect to the focal point of the beams (labelled 0 µm), such that the atoms experience different intensity environments at different z positions (labelled). Inset diagrams illustrate this translation of the atomic layer with respect to the focus. High intensities at the focus give rise to power broadening, which in combination with the changing collection efficiency and illumination area, also results in the changing count rates between spectra. Features in the TPFM spectra relate to the hyperfine 5P 3/2 states. Excitation beams had powers of 7 µW at 780 nm and 20 µW at 776 nm, with a Rayleigh range of approximately 4 µm. Each dataset had an integration time of 1-10 mins at a cell temperature of 65 • C.
stabilised to, as well as velocity selection and saturation effects. For example, for 85 Rb we observe a secondary resonance to the left of the main peak. This is due to contribution from a hyperfine level which is slightly offresonance with respect to the 776 nm laser. This peak appears shifted, and whilst for the purposes of this dataset no significant effort has been made to perfect the calibration of the spectra, we speculate that this is a shift akin to those seen in EIT studies [71]. However, the ability to preferentially excite certain hyperfine levels, as is apparent here, could prove useful for applications such as sensing.
The data in Fig. 8 clearly illustrates that the spectra are very sensitive to changes in position of the thin atomic medium. The observed modification of the spectra can be attributed to two effects. Firstly, power broadening causes broader spectral features closer to the focus (z = 0 µm) due to the higher intensities experienced by the atoms. Secondly, moving away from the focus alters the amount of fluorescence generated by the atoms (via changing intensity and illuminated area) and also collected by the objective lens, causing the changes in count rates observed. The spectra which do not strongly exhibit the effects of power broadening (for example those at z = ± 125 µm) also illustrate the benefit of nano-scale atomic confinement: narrow sub-Doppler fluorescence resonances are obtained in a co-propagating geometry as well as the counter-propagating one seen in Fig. 7. This allows for a compact scheme whereby a single objective delivers both excitation beams to a tightly focused spot in the atomic medium, as well as collecting the atomic fluorescence. In fact, a Voigt fit to the uppermost spectrum (z = 125 µm) yields a FWHM of (57.5 ± 0.6) MHz, the same order of magnitude as that achieved in the counterpropagating case. This is attributed to the velocity selection effects in nano-thickness vapors, which suppress spectral contributions from atoms with higher velocity components perpendicular to the cell walls. This allows sub-Doppler spectroscopy in geometries which would, in bulk vapors, produce Doppler-broadened spectra [31].
The TPFM method in the co-propagating geometry was also used to probe atomic vapor confined along a channel with a width and depth of 1 µm (shown in Fig. 9(a)). As displayed in Fig. 9(b), we find that a density gradient exists in the vapor as the fluorescence intensity reduces along the channel (with all other experimental parameters held constant between measurement sites). Given that this particular cell had been in operation for 1 year, it would be reasonably expected that an effective steady state had been reached in terms of atomic vapor distribution. However, as is shown by the decaying integrated count rate, this is not the case. Instead we have found that atomic vapor density is reproducibly not uniform along channels with confinement on lengthscales ≤ 1 µm. The vapor pressure is perturbed simply by the presence of tight confinement, a result which provides new and important insight into the diffusion properties of atoms inside nano-scale structures.
For the experiments reported in Fig. 9, the excitation beam powers used were a compromise between signal strength and power broadening. Hence by fitting Voigt profiles to the spectra we obtain an average FWHM of 140 MHz and, as illustrated in Fig. 9(c), show that the FWHM does not vary significantly between sites in this In this image the source of rubidium atoms (reservoir) is from the left, as indicated. TPFM spectra were recorded at various locations along this channel (indicated). All spectra were empirically fitted with Voigt profiles, and from these fits the (b) integrated count rates and (c) FWHMs are plotted as a function of position. An empirical exponential decay is fitted to the activity data (black dashed), which yields a characteristic decay length of (4±1) µm. Errorbars for both the activity and FWHM values were estimated using the functional approach [72]. (d) and (e) show two example spectra, color matched to the extreme points studied. This dataset was taken with powers of 50 nW at 780 nm and 776 nm, integration times of 0.5-9 hours, and a cell temperature of 60 • C) tight confinement regime. The observed power broadening alludes to the tight focus of the beam which delivers a high intensity even at the low powers used. In Fig. 9(d) and (e), we present spectra corresponding to the closest and farthest measurement points, which have FWHMs of (130 ± 10) MHz and (120 ± 20) MHz, respectively.
The TPFM method offers promise for the detection and study of low numbers of atoms confined to nanoscale structures. From the count rates observed in the spectrum shown in Fig. 9(e), we have extracted an estimate of the number of atoms excited to the 5D 5/2 state. Accounting for the efficiency and throughput of our detection setup, as well as the lifetime of the 5D 5/2 state, we estimate that the on resonance count rate observed corresponds to a mean value of just 0.01 atoms excited to the 5D 5/2 state within the detection volume. If instead we extract the atomic number density from the measured cell temperature and the rubidium vapor pressure curve, as is standard in experiments with bulk vapor cells [73], we find a mean ground state atom number of 1.5 within the same volume. This is consistent as we would expect that only a fraction of these are excited to the 5D 5/2 state, though further modelling is beyond the scope of this work.
Our data have also shown that it is possible to spectrally filter fluorescence signals from the TPFM method in such a way that the noise observed far off resonance, such as that in the spectra shown in Fig. 7 and Figs. 9(d) and (e), is consistent with the dark count rate measured for the photon-counting PMT used in this work. This dark count rate is approximately ≤ 5 cps, and our laser powers used lie in the range µW-nW. As such this method is highly sensitive, whilst also allowing for long integration times limited only by dark noise. Thus, given our demonstrated experimental versatility and considerable control over atom numbers through cell temperature and geometries, work towards interrogating low numbers of atoms is a promising avenue of further study.

V. CONCLUSION
We have designed and fabricated a nano-structured alkali-metal vapor cell that offers flexible optical access and high-NA imaging. Our glue-free design has proven to be durable and reliable, avoiding out-gassing and degradation of the internal atmosphere over time. The formation of nano-scale structures inside our cell, via direct write laser lithography and reactive ion etching, is flexible and highly customizable.
We have demonstrated the available optical access through the methods of TIRF and TPFM, which provide access to new regimes for atom-light interaction in tightly-confined vapors. We have discussed how the method of TIRF allows for fine control of the atomic excitation region on the nanometer-scale, and studied the transit-time broadening induced at this length-scale. We have also demonstrated TPFM as a high signal-to-noise dark-field measurement, and illustrated its potential for applications in sensing by studying the spectral response of the vapor layer to a spatially varying electric field. Finally, we have demonstrated TPFM for the detection of atoms confined by 1 µm in two dimensions as a novel method of studying the diffusion and spatial distribution of atoms in the thermal vapor phase. Through this method, we have demonstrated that tight confinement regimes modify the local vapor density, paving the way for development towards room temperature atom-based devices with close control of atom number at the level of single atoms.
The nanoscopic character of our vapor cell and the omnipresence of its walls readily provide sub-Doppler spectral resolution, giving access to individual hyperfine transitions of Rb. Other technical advantages of our cells include the integrated ITO heating system and the high excitation and collection efficiency of our high-NA approach, which allow for operating the chip at relatively low temperatures compatible with biological sensing. The combination of these features with high-NA lateral resolution and the ultrathin extent of the atoms makes our nano-cells a powerful spatially-selective sensing tool. A special example of current interest in sensing is magnetometry with nano-scale resolution [18], and indeed sensitive magnetometry has been recently demonstrated using nano-cells [15]. Our chip and measurement platform allows for greater spatial selectivity and high lateral resolution, especially for probing magnetic fields close to surfaces. The thin front panel and compactness of our design is a key benefit in this regard, but the bespoke nature of our fabrication process makes it possible, for example, to deposit material layers during cell manufacture which ultimately reside inside the finished cell, close to the atomic layer.
The architecture of our nano-cell makes it well adapted to the application of microscopy and spectroscopy techniques that are routine in nano-optics. As well as TIRF and TPFM, further potential examples include stimulated emission depletion (STED) fluorescence microscopy [74]; fluorescence correlation spectroscopy (FCS) [75]; and interferometric scattering (iSCAT) -a scheme which has been used previously to detect single nanoparticles and even charge transport via Rayleigh scattering [66,76]. These detection schemes, along with the versatility of the cell design and manufacturing process, offer access to a multitude of investigative routes. Further potential directions of study include the use of light-induced atomic desorption (LIAD) to locally modify the atomic vapor density, depositing micro-electrodes or micro-patterning structures such as waveguides or microring resonators within the nano-cells, or even adding dipole trapping to the setup [77]. Maturing the platform with integration of optical components to an on-chip design offers a promising route towards highly-scalable atom-based quantum technologies.