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a single two - level atom coupled to a single mode of an ideal optical cavity is described in the dipole and rotating wave approximations by the jaynes - cummings hamiltonian @xcite ( @xmath0 ) , @xmath1 here the operator @xmath2 annihilates a photon from the cavity field and @xmath3 is the pauli isospin operator lowering the atom from the excited state @xmath4 to the ground state @xmath5 , @xmath6 ( @xmath7 ) is the angular frequency of the uncoupled cavity resonance ( atomic transition ) , and the atom - field coupling constant , @xmath8 , is proportional to the atomic dipole moment and inversely proportional to the square root of the cavity mode volume . the hamiltonian ( [ eq : h ] ) conserves the total excitation number @xmath9 , and the simultaneous eigenstates of @xmath10 and @xmath11 consist of a dark ground state , @xmath12 obeying @xmath13 , and a ladder of doublets consisting of superpositions of @xmath14 and @xmath15 with @xmath16 , etc . figure [ fig : eigenfreqs](a ) shows the eigenvalues for the lowest doublet ( @xmath17 ) of the coupled system : @xmath18 the interaction lifts the degeneracy at @xmath19 , splitting the two levels in the eigenspectrum by @xmath20 at this point . in the time domain , this splitting corresponds to the rabi oscillation between the states @xmath21 and @xmath22 .     of the undamped hamiltonian @xmath10 . dashed lines : uncoupled atom ( blue ) , and cavity ( red ) . solid lines : avoided crossing of the eigenfrequencies @xmath23 of the dressed system , as given by eq.([eq : undampedeigens ] ) with @xmath24  mhz . colour indicates the relative amplitudes of the bare states @xmath21 ( more blue ) and @xmath22 ( more red ) in the eigenstate . ( b ) complex eigenvalues @xmath25 , given in eq.([eq : eigenfreqs ] ) for the non - hermitian effective hamiltonian @xmath26 , taking @xmath19 and @xmath27mhz . solid curves : eigenfrequencies @xmath28 . dashed curves : damping rates @xmath29 . zones ( i ) , ( ii ) and ( iii ) are discussed in the text.,title="fig:",width=154 ]   of the undamped hamiltonian @xmath10 . dashed lines : uncoupled atom ( blue ) , and cavity ( red ) . solid lines : avoided crossing of the eigenfrequencies @xmath23 of the dressed system , as given by eq.([eq : undampedeigens ] ) with @xmath24  mhz . colour indicates the relative amplitudes of the bare states @xmath21 ( more blue ) and @xmath22 ( more red ) in the eigenstate . ( b ) complex eigenvalues @xmath25 , given in eq.([eq : eigenfreqs ] ) for the non - hermitian effective hamiltonian @xmath26 , taking @xmath19 and @xmath27mhz . solid curves : eigenfrequencies @xmath28 . dashed curves : damping rates @xmath29 . zones ( i ) , ( ii ) and ( iii ) are discussed in the text.,title="fig:",width=154 ]    to describe real systems we need to account for decoherence processes affecting both the atom and cavity field . the probability for the bare atom to be in the excited state decays irreversibly through spontaneous emission at a rate @xmath30 , and the mean number of photons in the bare cavity decays at a rate @xmath31 due to transmission and losses at the mirrors . the three rates @xmath32 quantify the strength of the light - matter interactions through the dimensionless cooperativity @xmath33 . the cooperativity represents the effective optical depth of the atom @xcite , or the ratio of coherent scattering into the cavity mode to scattering into free space @xcite . when @xmath34 , single - atom detection is therefore possible either through the modified cavity spectrum or through laser - induced fluorescence driven from the side of the cavity @xcite . in the experiment we discuss here , @xmath35  mhz , @xmath36 varies from @xmath37@xmath38  ghz depending on mirror alignment ( see methods ) , and @xmath39 is continuously adjustable from zero up to @xmath40mhz as explained below , so the cooperativity @xmath41 can be large even though the rabi frequency is much smaller than one of the decay rates .        intuitively , one might expect that the avoided crossing of fig . [ fig : eigenfreqs](a ) would not be resolved in an experiment with @xmath42 because the underlying rabi oscillation between @xmath21 and @xmath22 would be interrupted by fast , irreversible cavity decay from @xmath22 to @xmath12 . to describe this quantitatively , we restrict ourselves to the hilbert sub - space spanned by the three lowest uncoupled states , @xmath43 , which is valid for weak excitation ( in the sense @xmath44 ) , and we account for dissipation through an effective hamiltonian @xcite , @xmath26 . the eigenvalues , @xmath25 , of this non - hermitian hamiltonian are complex : @xmath45 \label{eq : eigenfreqs}\end{aligned}\ ] ] the real parts of @xmath25 give the resonance frequencies of the coupled atom - cavity system , while the imaginary parts give the corresponding line widths . these are plotted in fig . [ fig : eigenfreqs](b ) as a function of @xmath8 for the case of @xmath19 . note that @xmath28 depends on the difference between the two uncoupled damping rates , so it is not generally the same as @xmath23 from eq.([eq : undampedeigens ] ) . in fig . [ fig : eigenfreqs](b ) we identify three distinct parameter regimes . in ( i ) , @xmath46 , i.e. the cooperativity @xmath47 , but @xmath48 . here , the real parts of @xmath25 are unshifted at @xmath49 and @xmath50 , and have widths of approximately @xmath51 and @xmath52 . these eigenmodes are primarily photonic and atomic , respectively , as reflected by the colouring of the lines in fig . [ fig : eigenfreqs](b ) . the appearance of @xmath41 in the line width of the atomic feature is a direct signature of the enhanced spontaneous emission rate of the atom , as first predicted by purcell @xcite . we therefore refer to this as the purcell regime ; this is the operating regime for all of the experiments described here . in region ( ii ) , above @xmath53 where there is an exceptional point @xcite , the eigenfrequencies separate and the damping rates merge to the mean value @xmath54 . some authors call this strong coupling , but the normal modes are not resolved until the splitting exceeds the width . this consideration gives rise to a second , more stringent definition of strong coupling , namely , ( iii ) : @xmath55 . in this regime , multiple rabi oscillations occur on average before the excitation decays . this definition of strong coupling is reminiscent of rayleigh s criterion defining the resolution limit of an imaging system under incoherent illumination , and is the definition which we adopt here . we now show that , when a coherent field probes the coupled system , quantum coherence between the atom and cavity can lead to quantum interference and narrow spectral features even in regime ( i ) , where our experiment lies . that is the main focus of this article .    in the laboratory , we excite the coupled atom - cavity system in two different ways . first , we probe the dressed cavity with coherent ( laser ) light through one of the mirrors , as illustrated in fig . [ fig : analogy](a ) . this adds a driving term to @xmath56 equal to @xmath57 . here @xmath58 , where @xmath59 is the number of photons per unit time driving the cavity mode and @xmath60 is the contribution of @xmath61 due to transmission through the input mirror @xcite . in the interaction picture rotating at the probe frequency @xmath62 , the equation of motion for the operator @xmath63 can be derived from the modified heisenberg evolution equation , @xmath64 $ ] , and similarly for @xmath2 : @xmath65 where @xmath66 and @xmath67 , and the detunings are defined by @xmath68 . here , we have assumed weak excitation of the atom , so that @xmath69 . the steady state solution for the amplitude of the ( coherent state ) field in the cavity @xmath70 is , @xmath71 so far , we have been considering a single atom with a fixed coupling @xmath8 to the cavity field , and therefore a fixed cooperativity . in the experiments however there is an ensemble of atoms simultaneously coupled to the cavity , and this results in a collective coupling @xmath72 , where @xmath73 is the volume integral of the atom number density , weighted by the intensity distribution of the cavity mode @xcite . the expression for @xmath70 in eq.([eq : ar ] ) remains valid as long as we understand @xmath8 to mean @xmath74 . figure  [ fig : analogy](c ) shows the mean number of photons in the cavity as a function of laser - cavity detuning @xmath75 . the photon number @xmath76 is scaled by @xmath77 in order to obtain a curve that is independent of the probe strength @xmath78 . the atom - cavity coupling is most pronounced when the atom and the cavity resonate simultaneously with the driving field , so we have set @xmath19 here . the wide double peak ( red ) is calculated for @xmath79ghz , which lies in the region of strong coupling , indicated by ( iii ) in fig .  [ fig : eigenfreqs](b ) . this curve shows the two spectroscopically - resolved , coupled atom - cavity states . the curve with a narrow central dip ( blue ) has the coupling reduced to @xmath80mhz ( @xmath81 ) , which places it at the left of zone ( i ) in fig . [ fig : eigenfreqs](b ) . the two eigenvalues are not spectroscopically resolved in the sense of region ( iii ) , but they are still apparent as a broad peak with a narrow hole , made visible by quantum coherence .    the spectra in fig . [ fig : analogy](c ) can also be understood in the language of eit , as was previously noted @xcite for the complementary case where @xmath82 . interest in the transition from eit to autler - townes splitting has recently grown @xcite , partly owing to the wide variety of physical systems which exhibit formally similar dynamics @xcite . in our cavity qed system , this transition is manifest as the passage from dit to strong coupling . the analogy between dit and conventional eit is illustrated in fig . [ fig : analogy](e ) . depending on the detuning between the cavity and atomic resonances , the three lowest dressed states of the cavity qed system form either ladder- or @xmath83-type configurations . in this analogy the cavity plays the role of the absorber , with the atomic dipole ( proportional to @xmath84 ) acting as the coupling field which induces the transparency . the cavity field ( proportional to @xmath85 ) drives the @xmath86 transition , whose ` natural ' line width is set by the cavity damping rate , @xmath61 , and the vacuum - induced coupling on @xmath87 is subject to dephasing at the rate @xmath88 , returning the system to the absolute ground state @xmath12 . whether the dressed system maps onto a ladder or @xmath83 configuration depends on the cavity - atom detuning and the method of probing . for our case , where @xmath89 , direct cavity probing exhibits a narrow dit window with a sub - natural line width equal to @xmath90 . in this expression we can identify @xmath91 as the coherent scattering rate predicted by purcell and @xmath88 as an effective dephasing rate . as long as the former exceeds the latter , meaning precisely that @xmath41 exceeds 1 , a transparency window emerges in the cavity spectrum . similarly , the depth of this window depends on @xmath41 , and we are able to observe these effects experimentally because we can adjust the cooperativity in the regime where @xmath92 by varying the density of atoms in the cavity .    in a second method of probing the coupled system , we drive the atoms  rather than the cavity  by illuminating them with a near - resonant beam propagating transverse to the cavity axis , as illustrated in fig . [ fig : analogy](b ) . this amounts to setting @xmath93 and adding a term @xmath94 to the hamiltonian @xmath56 , with @xmath95 being the probe rabi frequency . the corresponding steady - state solution for the cavity field is then , @xmath96 figure  [ fig : analogy](d ) shows the calculated number of photons in the cavity for this configuration as a function of the same laser frequency scan , again with @xmath19 . in this case we have scaled the photon number by @xmath97 to obtain a curve that is independent of the probe strength @xmath95 . the narrow resonance at @xmath80mhz ( @xmath81 , blue ) does not reveal that the system has two modes , and even with strong coupling at @xmath79ghz ( red ) , the normal modes are barely resolved , in contrast with the cavity - probed case . in the dit language , the roles of atom and cavity are interchanged here , with the atoms acting as the absorber . now the cavity field in fig . [ fig : analogy](d ) shows no dit effect even when the condition @xmath47 is satisfied , because the dephasing rate is equal to @xmath61 and the condition @xmath98 prevents the formation of a transparency window in the @xmath99 transition @xcite .      in the experiment we measure the flux of photons travelling from the cavity to a single photon counting module ( methods ) . this flux , @xmath100 , is related to the intracavity field amplitude , @xmath70 : @xmath101 where @xmath102 is the power reflection coefficient of the intput - output coupling mirror and @xmath103 is that of the back mirror . here we have used the fact that @xmath104 , and that losses at mirror 1 are negligible compared to transmission in our experiment . we first consider the case of fig . [ fig : analogy](a ) , where the cavity is probed directly . the upper row in fig . [ fig : refl ] shows the number of photons detected per ms versus @xmath105 and @xmath75 for values of cooperativity ranging from @xmath106@xmath107 . the cooperativity was varied by changing the intra - cavity density of atoms , and @xmath41 was determined by fits to the spectra ( shown in the bottom row ) , with the amplitude as the only other fit parameter . for these measurements , resonances of the coupled system are manifest as minima in the detected photocount rate as described by eqs.([eq : ar ] ) and ( [ eq : flux ] ) . despite always operating in a regime where the cavity damping rate exceeds the rabi frequency by an order of magnitude , the coherent effect of the atomic dipole is evident as soon as @xmath108 . in particular it is seen that the reflection minima trace out the avoided crossing of the eigenvalues ( [ eq : undampedeigens ] ) of the undamped hamiltonian , satisfying the condition @xmath109 . that the locations of these features are described independently of the decoherence rates @xmath88 and @xmath61 emphasizes the fact that the underlying coherent properties of the system have been revealed , despite the absence of rabi oscillations .        in the experimental configuration depicted in fig . [ fig : analogy](b ) the coupled system is probed via scattering of incoming radiation by the atoms : the atomic dipole is driven by the probe beam from the side of the cavity and emits radiation at the same frequency into the resonator . according to eq.([eq : flux ] ) with @xmath110 , the built up cavity field is transmitted through the coupling mirror , producing a steady - state flux of @xmath111 photons per unit time , with @xmath70 given by eq.([eq : af ] ) and @xmath112 in our system . the detected photon count rate is shown in the upper row of fig . [ fig : fluo ] . the values of @xmath41 here are lower than in reflection for comparable atomic densities because the side - driven atoms are more weakly coupled to the cavity mode @xcite . for values of @xmath113 , the emission spectrum is localised around the origin of the @xmath75@xmath105 plane . comparing eqs.([eq : ar ] ) and ( [ eq : af ] ) , we see that the driven atoms act as a secondary probe source exciting the cavity field with relatively small line width , @xmath88 : @xmath114 as @xmath41 is increased , the atom - cavity coupling leads to a characteristic ` butterfly ' shape in the cavity emission spectrum . the central feature is split into two broad maxima along the scaled diagonal defined by @xmath115 , centred around @xmath116 . in contrast with the reflection spectra , the eigenvalues of the undamped hamiltonian are not clearly reflected in the split fluorescence resonances . with the cooperativity and the amplitude of the signal as the only free parameters , we fit eq.([eq : af ] ) to our experimental data . the results are shown in the bottom row of fig . [ fig : fluo ] .        despite the fact that fluorescence measurements do not exhibit dit , both probe configurations exhibit the same spectral width when the cavity resonance frequency is tuned to that of the atom in free space ( @xmath117 ) . this corresponds to nearly vertical traces through the plots in figs . [ fig : refl ] and [ fig : fluo ] . along these traces , both types of spectra are well approximated by simple lorentzians , and the spectral width @xmath118 is obtained as the half - width at half - maximum of a fit to such . the results are shown in fig . [ fig : width ] , plotted against the cooperativity @xmath41 obtained from the full surface fits . the solid curve is the expectation @xmath119 with no free parameters . this is just the imaginary part of @xmath120 , plotted in fig . [ fig : eigenfreqs](b ) as the lower ( blue dashed ) branch . for the reflection measurements we understand this peak as the dressing - induced transparency window described above , having a deeply sub - natural line width associated with the coherent coupling rate @xmath8 . for fluorescence , the atoms scatter coherently into the cavity mode at a rate equal to @xmath91 through the purcell effect . following the abrupt shut - off of a resonant probe laser , one would observe that the intracavity power would decay exponentially at a rate @xmath121 for times longer than @xmath122 . the fact that this decay is much slower than the bare cavity ring - down rate shows that the relatively long coherence time of the atoms effectively inhibits the decay of the coupled system .     versus cooperativity @xmath41 for the reflection and fluorescence spectra with @xmath117 . the lorentzian half - widths at half - maximum are normalized to the natural atomic line width @xmath88 , and error bars show the fit uncertainty . the dashed line is the asymptotic value @xmath88 , while the solid line shows the prediction @xmath123.,scaledwidth=48.0% ] we have presented an experimental study of coherence within an overdamped quantum system consisting of two - level atoms coupled to an optical microcavity . despite the absence of rabi oscillations in our system , the cavity reflection signal reveals the avoided crossing associated with the eigenvalues of the undamped hamiltonian . we note that the response of the intracavity field to a probe beam is formally identical to that of a three level atom in free space exhibiting electromagnetically induced transparency . this sheds new light on the persistent role of coherence in the so - called ` bad cavity ' regime of cavity qed . we prefer to call this the ` fast cavity ' regime . we have also shown that , although this dit effect is intrinsically absent when the atoms are driven directly from the side of the cavity , both experimental configurations produce a split spectrum when the cooperativity becomes large enough . the formal mapping onto eit also suggests a range of applications for fast cavity qed with cold atoms on hybrid atomic - photonic chips . these include dipole - induced switching @xcite and optical pulse lag / lead circuits @xcite . in the absence of atoms , a resonant cavity provides a group delay of @xmath122 in transmission ; as the coupling @xmath8 is increased , the delay is reduced and becomes a superluminal _ advance _ approaching @xmath124 for @xmath125 ( methods ) . the apparatus has been described previously @xcite , so will only be summarised here . a magneto - optical reflection trap ( reflection - mot ) , formed above a gold mirror , collects a few million @xmath126 atoms in a cloud of approximate size @xmath127 . the cloud is released , cooled further in sub - doppler optical molasses , then pushed with a pulsed resonant laser beam through a 1 mm hole in the mirror and into the optical microcavity , which lies approximately 5 mm below . the microcavity itself is a plano - concave fabry - prot resonator , built as described in @xcite . the plane mirror is a multi - layer dielectric stack that we have glued onto the tip of a cleaved single - mode optical fibre . this mirror serves as the input - output coupling mirror . the second mirror is one of an array of approximately spherical micro - mirrors with @xmath128 m radius of curvature on an etched and dielectric - coated silicon wafer . the cavity length is tuned around @xmath129 m using a shear piezo on which the fibre mirror is mounted , and is stabilised with a side - of - fringe technique using light from a single - frequency ti : sapphire laser ( coherent , mbr-110 ) operating at @xmath130 nm . the wavelengths of both locking and probing lasers are monitored with a wavemeter ( highfinesse , ws6 ) . the cavity finesse varies slightly throughout the measurements presented here due to a slow drift in the mirror alignment . the finesse ( linewidth @xmath36 ) is 260 ( @xmath37  ghz ) in fig . [ fig : refl ] , and 180 ( @xmath38  ghz ) in fig . [ fig : fluo ] . the fringe contrast , defined by @xmath131(min power)/(max power ) throughout a cavity scan , is above 95% for all of the measurements . near - resonant signal light from the cavity is separated from the locking light and incoming probe light using a 90/10 beam splitter and a series of dichroic filters , and detected on a single - photon counting module ( perkin - elmer , spcm - aqr-14 ) . the detected counts are corrected for dead time at high flux rates with a polynomial formula as specified by the manufacturer . the group delay @xmath132 corresponding to transmission through a cavity can be obtained from the cavity transfer function via @xmath133 taking @xmath70 in eq.([eq : ar ] ) with @xmath117 , and taylor expanding around resonance , one obtains @xmath134 giving the limits @xmath135 the sign of the group delay for the dressed cavity in dit is opposite to that in conventional eit , where @xmath132 becomes large and positive as the transparency is increased . in the strong dit limit ( with @xmath136 ) , one recovers the relatively large group advance , equal to @xmath124 , that an atomic medium with equivalent optical depth would produce in free space . as in free space , there is an intrinsic compromise between group dispersion and transmission in this limit of dit , due to the suppression of the latter when @xmath41 becomes large . 99    ramsey , n. f. experiments with separated oscillatory fields and hydrogen masers . _ * 62 * , 541553 ( 1990 ) . ludlow , a. d. , boyd , m. m. , ye , j. , peik , e. & schmidt , p. o. optical atomic clocks . phys . _ * 87 * , 637701 ( 2015 ) . cronin , a. d. , schmiedmayer , j. & pritchard , d. e. optics and inteferometry with atoms and molecules . phys . _ * 81 * , 10511129 ( 2009 ) . hornberger , k. , gerlich , s. , haslinger , p. , nimmrichter , s. & arndt , m. colloquium : quantum interference with clusters and molecules . phys . _ * 84 * , 157173 ( 2012 ) . see , for example , the supplement on quantum coherence , _ nature _ * 453 * , 10031049 ( 2008 ) . zurek , w. h. decoherence , einselection , and the quantum origins of the classical . phys . _ * 75 * , 715775 ( 2003 ) . schlosshauer , m. decoherence , the measurement problem , and the interpretations of quantum mechanics . phys . _ * 76 * , 12671305 ( 2004 ) . rice , p.r . & brecha , r.j . , cavity induced transparency . _ optics communications_*126 * , 230 - 235 ( 1996 ) . shimizu , y. , shiokawa , n. , yamamoto , n. , kosuma , m. , kuga , t. , deng , l. & hagley , e. w. control of light pulse propagation with only a few cold atoms in a high - finesse microcavity . _ * 89 * , 233001 ( 2002 ) . wang , h. , goorskey , d. j. , burkett , w. h. & xiao , m. cavity - linewidth narrowing by means of electromagnetically induced transparency . _ * 25 * , 17321734 ( 2000 ) . hernandez , g. , zhang , j. & zhu , y. vacuum rabi splitting and intracavity dark state in a cavity - atom system . rev . a _ * 76 * , 053814 ( 2007 ) .    mcke , m. , figueroa , e. , bochmann , j. , hahn , c. , murr , k. , ritter , s. , villas - boas , c. j. & rempe , g. electromagnetically induced transparency with single atoms in a cavity . _ nature _ * 465 * , 755758 ( 2010 ) . kampschulte , t. , alt , w. , brakhane , s. , eckstein , m. , reimann , r. , widera , a. & meschede , d. optical control of the refractive index of a single atom . lett . _ * 105 * , 153603 ( 2010 ) . albert , m. , dantan , a. & drewsen , m. cavity electromagnetically induced transparency and all - optical switching using ion coulomb crystals . phot . _ * 5 * , 633636 ( 2011 ) . tanji - suzuki , h. , chen , w. , landig , r. , simon , j. & vuleti , v. vacuum - induced transparency . science * 333 * , 12661269 ( 2011 ) . purcell , e. m. spontaneous emission probabilities at radio frequencies . . rev . _ * 69 * , 681 ( 1946 ) . jaynes , e. e. & cummings , f. w. comparison of quantum and semiclassical radiation theories with application to the beam maser . _ proc . of the ieee _ * 51 * , 89 - 109 ( 1963 ) . horak , p. , klappauf , b. g. , haase , a. , folman , r. , schmiedmayer , j. , domokos , p. & hinds , e. a. possibility of single - atom detection on a chip . a _ * 67 * , 043806 ( 2003 ) . thompson , r. j. , rempe , g. & kimble , h. j. observation of normal mode splitting for an atom in an optical cavity . lett . _ * 68 * , 1132 - 1135 ( 1992 ) . wilzbach , m. , heine , d. , groth , s. , liu , x. , raub , t. , hessmo , b. & schmiedmayer j , simple integrated single - atom detector . _ * 34 * , 259 - 261 ( 2009 ) . teper , i. , lin , y .- j . & vuleti , v. resonator - aided single - atom detection on a microfabricated chip . lett . _ * 97 * , 023002 ( 2006 ) . trupke , m. , goldwin , j. , darqui , b. , dutier , g. eriksson , s. , ashmore , j. & hinds , e. a. atom detection and photon production in a scalable , open , optical microcavity . lett . _ * 99 * , 063601 ( 2007 ) . goldwin , j. , trupke , m. , kenner , j. , ratnapala , a. & hinds , e. a. fast cavity - enhanced atom detection with low noise and high fidelity _ nat . * 2 * , 418 ( 2011 ) . see eq.(18 ) and ref . [ 9 ] of hegerfeldt , g. c. , how to reset an atom after a photon detection . a. _ * 47 * , 449 ( 1993 ) . t. kato , perturbation theory of linear operators , " springer , berlin ( 1966 ) . carmichael , h. j. & sanders , b. c. multiatom effects in cavity qed with atomic beams . a _ * 60 * , 2497 - 2504 ( 1999 ) . anisimov , p. m. , dowling , j. p. & sanders , b. c. objectively discerning autler - townes splitting from electromagnetically induced transparency . lett . _ * 107 * , 163604 ( 2011 ) . peng , b. , zdemir ,  . k. , chen , w. , nori , f. , & yang , l. what is and what is not electromagnetically induced transparency in whispering - gallery microcavities . _ nature comm . _ 5:5082 doi : 10.1038/ncomms6082 ( 2014 ) . souza , j. a. , cabral , l. , oliveira , r. r. & villas - boas , c. j. electromagnetically - induced - transparency - related phenomena and their mechanical analogs . rev . a _ * 92 * , 023818 ( 2015 ) .    fleischhauer , m. imamoglu , a. & marangos , j. p. , electromagnetically induced transparency : optics in coherent media . phys . _ * 77 * , 633 ( 2005 ) . waks , e. & vukovi , j. dipole induced transparency in drop - filter cavity - waveguide systems . _ lett . _ * 96 * , 153601 ( 2006 ) . faraon , a. , fushman , i. , englund , d. , stoltz , n. petroff , p. & vukovi , j. dipole induced trasnparency in waveguide coupled photonic crystal cavities . _ _ * 16 * , 1215412162 ( 2008 ) . rao , v. s. c. m. , gupta , s. d. & agarwal , g. s. atomic absorbers for controlling pulse propagation in resonators . * 29 * , 307309 ( 2004 ) .    trupke , m. , hinds , e. a. , eriksson , s. , curtis , e. a. , moktadir , z. , kukharenka , e. & kraft , m. microfabricated high - finesse optical cavity with open access and small volume . lett . _ * 87 * , 211106 ( 2005 ) . this work was funded by the eu ( fp-7 grant 247687 ) , by the uk epsrc , and by the royal society . m.s . acknowledges financial support from the austrian science fund ( dk coqus project no .  w 1210-n16 ) and m.m .  from the stiftung der deutschen wirtschaft ( sdw ) . we thank jon dyne and val gerulius for technical expertise , and michael trupke , joanna kenner , and martin everett for early contributions to the apparatus . we gratefully acknowledge stimulating discussions with shuang zhang and the late wolfgang lange . the experiments were conceived and supervised by j.g .  and e.a.h . data were obtained by y .- h.l .  with the help of g.b . , m.s . , and m.m . , and analysed by y .- h.l .  and g.b . all authors contributed to writing and editing the manuscript . the authors declare no competing financial interests .
it is usually considered that the spectrum of an optical cavity coupled to an atomic medium does not exhibit a normal - mode splitting unless the system satisfies the  strong coupling " condition , meaning the rabi frequency of the coherent coupling exceeds the decay rates of atom and cavity excitations . 
 we show that this need not be the case , but depends on the way in which the coupled system is probed . 
 measurements of the reflection of a probe laser from the input mirror of an overdamped cavity reveal an avoided crossing in the spectrum which is not observed when driving the atoms directly and measuring the purcell - enhanced cavity emission . 
 we understand these observations by noting a formal correspondence with electromagnetically - induced transparency of a three - level atom in free space , where our cavity acts as the absorbing medium and the coupled atoms play the role of the control field . 
 the oscillatory dynamics intrinsic to quantum systems can be harnessed in a number of ways for advanced applications in metrology and sensing . 
 coherent oscillations among quantum states are at the heart of existing time - frequency standards @xcite , atom interferometers @xcite , and quantum information processors @xcite . 
 coherence in these systems is ultimately limited by dephasing which arises from the coupling of the isolated quantum system to the vast reservoir of states representing the environment . in some cases 
 the system is _ open _ by design , for example to allow communication of information into and out of the system ; in other cases it is unavoidable , due to losses or the influence of uncontrolled fluctuations in the reservoir . 
 the exact role of decoherence in the transition from microscopic quantum to macroscopic classical behaviour remains an active field of study @xcite . 
 here we study a system comprising cold atoms coupled to a high finesse optical microcavity . 
 the relatively small cavity mode volume results in a large electric dipole coupling between a single photon and an atom . 
 this comes at the price of a fast optical decoherence rate due to transmission and losses from the cavity mode into external modes . despite this , 
 we show how the hamiltonian eigenstates of the system can be revealed through spectroscopic measurements . by probing the cavity with an incident field , we realize an analogy to electromagnetically induced transparency ( eit ) in which the coherent atom - cavity coupling plays the role of the control field . the effective three - level system is formed by the lowest triplet of dressed states of the coupled atom - cavity complex . 
 we refer to this as _ dressing - induced transparency _ ( dit ) , and it is complementary to cavity - induced transparency as proposed in @xcite , with the roles of cavity and atom here reversed . 
 the sub - natural width of the dit window depends on the coherent atom - cavity coupling strength . because of this , we are able to observe an avoided crossing in the dressed cavity spectrum , usually taken as evidence of strong coupling , despite the complete overdamping of rabi oscillations in our experiment . 
 we also control the width of the dit window through the density dependence of the atomic dipole . 
 the analogy to eit also highlights the existence of steep dispersion present in the system @xcite . 
 in contrast with conventional eit of three - level atoms in optical cavities @xcite , it is possible in our system to swap the roles of longitudinal and transverse dephasing rates , corresponding to decay of populations and coherences , respectively . when the probe laser is incident on the atoms directly ( from the side of the cavity ) , dit per se is not present . 
 however , the spectral width of the narrow feature in this case is the same as for the dressing - induced transparency window with the same parameters , casting new light on the well - known purcell effect describing coherent scattering into the cavity mode @xcite . 
 our results show that even in a highly overdamped regime , quantum interference can be used to reveal aspects of the coherent coupling .