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surface plasmon polaritons have been used for a long time as sensitive detectors e.g. for biomolecules .
this is mainly done in the so - called kretschmann configuration by internal reflection of a laser beam from a surface that is coated with a thin metal film kretschmann_radiative_1968 .
particles that are close to or stick to the metal film can be detected via their optical properties which shift the surface plasmon angle @xmath1 under which a spp can be excited . in principle
, such shifts can be detected very sensitively by measuring the phase of the reflected light beam which , at the plasmon angle , changes dramatically .
however , the fact that the reflectivity is zero at the plasmon angle , i.e the power of the laser beam is completely transferred into a plasmonic excitation , broadens the detectable phase shift and limits the sensitivity @xcite .
recently , a new excitation scheme has been introduced which avoids this problem by an electronic feedback on the phase of the incident laser field @xcite . in the work presented here ,
this scheme is used for the first time to actually measure the optical properties of a sample . the work is mainly motivated by recent progress in the field of surface quantum optics , atom chips and hybrid quantum systems .
such tailored quantum systems made of cold atoms near nanostructured surfaces are expected to open up new opportunities for the construction of quantum sensors and for quantum information . in this context , we recently studied clouds of ultracold atoms coupled to evanescent waves near solid surfaces @xcite .
the enhancement of such optial near - fields by the excitation of surface plasmons is already known for some time @xcite , but only recently , proposals have been put forward to generate plasmonic nanopotentials for the manipulation and trapping of cold atoms chang_trapping_2009 , murphy_electro - optical_2009 . for the design of such traps , surface potentials such as casimir - polder potentials casimir_influence_1948 have to be taken into account and some effort has been invested by the cold atoms community for studying dissipative forces @xcite . however ,
additional potentials from particles adsorbed at the surface are only little considered . as has been shown experimentally mcguirk_alkali - metal_2004 , such potentials can dramatically influence atom traps near surfaces . thus it is crucial to understand and control atomic adsoption , e.g. by laser - induced atomic desorption ( liad ) meucci_light - induced_1994 .
furthermore , fascinating ideas have been proposed that rely on the controlled adsorption of atoms on semiconductor surfaces , which might prove as an important technological step towards the manipulation of electronic nano devices @xcite .    here
, we report on adsorption of thermal rubidium atoms on a gold nanofilm .
the rubidium coverage is monitored by the phase shift in the excitation spectrum of surface plasmon polaritons . by rapidly changing the rubidium vapor pressure ,
the balance between adsorption and thermally induced desorption is perturbed and reequilibration is monitored in real time .
the observations are compared to a simple langmuir type model and the parameters of the model are extracted from the data .
the ad- and desorption of rubidium atoms is observed by phase sensitive detection of the surface plasmon resonance .
the experimental setup is shown in figure  [ fig : opt_el_aufbau ] .
the beam from a grating stabilized diode laser ( laser 1 , wavelength near the d2-line of @xmath2 at @xmath3  nm , laser power @xmath4  mw , laser bandwith @xmath5  mhz ) is internally reflected from the gold - coated surface of a dielectric prism . the incident angle @xmath6 at which the laser hits the prism surface can be adjusted with a mirror mounted onto a mechanically driven translation stage ( ts ) .
it shifts the beam relative to a lens which guides the beam to the prism surface .
the position of the translation stage is monitored with an auxiliary laser beam and a position - sensitive diode ( psd ) .
the guiding lens is the second lens in a @xmath7 telescope with the first lens being attached to the translation stage . by
that the incident beam is collimated at the prism surface . at a characteristic plasmon angle @xmath8 surface plasmons
are excited by the p - polarized fraction of the incoming light .
the incident light is absorbed by the plasmon excitation and the reflectivity for p - polarized light @xmath9 drops to a minimum ( figure  fig : refl_phase ) .
if rubidium atoms are adsorbed , the value of the plasmon angle shifts and the phase of the p - polarized fraction of the reflected light field @xmath10 changes .
this phase change is monitored with a standard hnsch couillaud ( hc ) setup hansch_laser_1980 .
a pi - servo electronics feeds the signal to an electro - optic modulator ( eom ) that controls the phase of the incident laser light @xcite .
this locks the hnsch couillaud signal to zero such that the control - voltage at the eom is directly proportional to @xmath10 .
the gold film on the prism surface has been fabricated by e - beam evaporation and has a thickness of approximately @xmath11 .
below the gold film a very thin layer of titanium has been added for improving adhesion of the gold to the glass substrate .
the prism is placed inside a vacuum chamber at a base pressure of @xmath12 and is mounted to a temperature controlled heating .
the partial pressure of rb in the chamber is controlled by a resistively heated dispenser and can be raised within a few seconds up to several @xmath13 .
laser induced desorption of rb atoms can be investigated with an additional blue laser beam at a wavelength near 406 nm and a maximum power of 20 mw ( laser 2)@xcite .
the interpretation of our experiment is based on the observation that , according to brunauer , emmet and teller ( bet ) , only fractions of a monolayer can be adsorbed if the vapor pressure of an adsorbant is smaller than the saturation vapor pressure @xmath14 @xcite .
thus the surface coverage @xmath15 only takes values between @xmath16 and @xmath17 , i.e. @xmath18 .
we model the temporal change of the surface coverage by the rate equation @xmath19with a desorption constant @xmath20 , an inpinging flux of atoms on the surface @xmath21 , a typical area per adsorbed atom of @xmath22 and a sticking probability @xmath23 .
the atomic flux hitting the surface is given by @xmath24 with the factor @xmath25 following from integrating the knudsen cosine law over a half sphere , the ideal gas vapor density @xmath26 and the thermal velocity of the atoms @xmath27 .
for simplicity we define the flux per pressure @xmath28 in units of adsorbed monolayers via @xmath29 , i.e. @xmath30 . the sticking probability is taken from the langmuir model @xmath31 , with the initial sticking probability @xmath32 @xcite .
note that @xmath23 vanishes for full coverage ( @xmath33 ) .
this guaranties that only fractions of a monolayer can be adsorbed . with these definitions ( [ eq : rate_eq_1 ] ) reads @xmath34 in equilibrium ( @xmath35 ) the surface coverage is given by @xmath36the equilibrium coverage depends on the pressure in the chamber .
if the pressure is rapidly changed the new equilibrium is exponentially reached within an @xmath37-timescale @xmath38as can be deduced from ( [ eq : rate_eq_2 ] ) .
we measure the adsorption of rubidium with the above mentioned setup by two different methods . in the first method
the incidence angle is scanned and from the obtained signal the position of the plasmon angle is determined .
this method is applicable for a plasmon angle which changes only little during the scan time of approximately one minute .
figure  [ fig : scans ] shows an example .
the relation between the shift of the plasmon angle @xmath39 and the thickness of the adsorbed layer @xmath40 is taken from a four - layer matrix model ( layer 1 : glass substrate , layer 2 : gold film , layer 3 : rb adsorbate , layer 4 : vacuum ) which takes multiple reflections at the boundaries into account @xcite . with the dielectric constant of gold @xmath41 and rb @xmath42 @xcite
the result is @xmath43 .
the observed shift of the plasmon angle in figure  [ fig : scans ] of @xmath44 thus corresponds to an adsorbed rb layer thickness of @xmath45  nm .
the second , more sensitive method records the phase @xmath10 with the incidence angle held fixed at the plasmon angle .
adsorption and desorption of atoms can now be observed in real time by looking at the temporal change of the phase @xmath10 . for not too large variations of @xmath46
the relation between plasmon angle and phase is linear with a slope of @xmath47rad@xmath48 that is taken from the left curve in figure  [ fig : scans ] .
note that after adsorption of rb ( right curve ) the slope is with @xmath49 slightly smaller . for large changes of the plasmon angle the working point
is shifted from the linear regime to a regime where the phase change saturates .
thus the second method can only be applied for small changes of the plasmon angle , unless the incidence angle is recalibrated .
typical data are shown in figure  [ fig : adsorption_phase ] . in ( a )
the rb vapor pressure is quickly increased by activating the dispenser for about 80s ( curve ( ii ) ) .
the pressure is determined with a standard ion - gauge . curve ( i ) shows the resulting change of the phase @xmath50 . during the pulsed increase of the vapor pressure
the rubidium coverage also grows and remains at an increased value after the puls .
figure  [ fig : adsorption_phase ] ( b ) shows a similar measurement with higher resolution which allows to estimate the sensitivity of the method .
after low pass filtering the signal with an integration time of @xmath51  ms the noise of the phase signal is on the order of @xmath52  rad . at this noise level
the uncertainty of the measured layer thickness is @xmath53  pm . with an average distance between two atoms given by twice the covalent radius of rb of @xmath54  pm
, the sensitivity amounts to better than @xmath55 of an adsorbed monolayer .
this sensitivity corresponds to a resolveable relative refractive index change of @xmath56 .    in the experiment
the gold surface is heated to a temperature of @xmath57  c .
the resulting rb saturation vapor pressure of @xmath58  mbar is one order of magnitude larger than the maximum rb vapor pressure in the experiment of @xmath59  mbar .
the above assumption of a fractional coverage is thus well justified . in figure
[ fig : desorption_angle ] the observed coverage @xmath60 is plotted during and after a temporal increase of the rb vapor pressure . during the first 20 min the pressure stays very much near a value of about @xmath61  mbar . the coverage growth rate at this pressure can be derived by linearly extrapolating the coverage increase with time .
we obtain @xmath62 . putting this value into ( [ eq : rate_eq_2 ] ) and setting @xmath63
the initial sticking coefficient can be determined to be @xmath64 .
after @xmath65 min we reduce the pressure back to a value of @xmath66  mbar . now the atoms thermally desorb and the coverage decays exponentially .
the thermal desorption constant @xmath67 can be determined from ( [ eq : tau ] ) by measuring the 1/e decay time @xmath68 .
fitting an exponential curve to the data yields @xmath69
s. for the desorption constant we obtain @xmath70 . in order to show the consistency of the model with the determined parameters the equilibrium coverage is calculated from ( eq : coverage_gg ) to be @xmath71 .
this value is comparable to the observed value in figure  [ fig : desorption_angle ] of @xmath72 .
the equilibrium coverage can be further reduced by exposing the surface to a laser beam with a wavelength near @xmath73 ( @xmath74 laserpower , beam diameter @xmath17  mm ) .
figure  [ fig : desorption_laser ] shows the resulting change of the surface coverage @xmath75 .
as soon as the blue laser is turned on , the coverage decreases in time with a rate of @xmath76 .
the total desorption coefficient is now the sum of the thermal and the laser - induced desorption coefficient @xmath77 . with ( [ eq : rate_eq_2 ] ) and for @xmath78 and a pressure of @xmath79
mbar the total desorption coefficient amounts to @xmath80 .
this results in a pure laser - induced desorption rate of @xmath81 at a laser power of @xmath74 .
the new equilibrium coverage of @xmath82 is reached witin a @xmath37  time of @xmath83  s.
we have applied a recently introduced method @xcite for detecting de- and adsorption phenomena by means of phase - sensitive detection of a surface plasmon resonance to rubidium on a gold surface .
adsorption and desorption of rb were observed and interpreted with a rate model .
we reach a sensitivity of better than @xmath0 of a monolayer , respectively a refractive index unit change of @xmath84  riu within an integration time of @xmath85  ms .
this is comparable to typical sensitivities reached with surface plasmon resonance sensors @xcite .
the observed sensitivity in this paper is limited by technical noise which leaves much room for substantial improvement , e.g. by a shot - noise limited detection scheme , by suppression of laser frequency noise , and by longer integration time . as has been shown in @xcite , a resolution of @xmath86  riu within an integration time of @xmath87  s seam feasible even far above the shot - noise limit .
such a sensitivity exceeds the best values reported for converntional detectors , e.g. in @xcite . by comparing the experimental data with a langmuir type adsorption model we find a desorption constant of @xmath88 and an initial sticking probability @xmath64 .
laser - assisted desorption has been observed .
a desorption coefficient of @xmath89 is determined for a laser power of @xmath90  mw .
we acknowledge financial support by the dfg within the euroquasar program of the esf and thank a. hemmerich for inspiring discussions .
99 knig t , weidemller m and hemmerich a 2008 _ appl .
b _ * 93 * 545
hybrid quantum systems made of cold atoms near nanostructured surfaces are expected to open up new opportunities for the construction of quantum sensors and for quantum information . for the design of such tailored quantum systems 
 the interaction of alkali atoms with dielectric and metallic surfaces is crucial and required to be understood in detail . here 
 , we present real - time measurements of the adsorption and desorption of rubidium atoms on gold nanofilms . 
 surface plasmon polaritons ( spp ) are excited at the gold surface and detected in a phase sensitive way . from the temporal change of the spp phase the rubidium coverage of the gold film 
 is deduced with a sensitivity of better than @xmath0 of a monolayer . by comparing the experimental data with a langmuir type adsorption model we obtain the thermal desorption rate and the sticking probability . 
 in addition , also laser - induced desorption is observed and quantified .