When a resonant photon traverses a sample of absorbing atoms, how much time do atoms spend in the excited state? Does the answer depend on whether the photon is ultimately scattered vs. transmitted? In particular, if it is not scattered, meaning that it emerges in the direction it entered, does it cause atoms to spend any time in the excited state, and if so, how much? In this thesis, I report an experimental measurement of the time a transmitted photon causes atoms to spend in the excited state. The experiment is carried out in an ultra-cold gas of Rubidium 85 atoms and involves simultaneously recording changes to the excited state occupation number induced by incident ("signal") photons and whether those photons are transmitted. The time atoms spend in the excited state, which is defined in terms of the time integral of the average excited state occupation number, is measured weakly using a separate, off-resonant “probe” laser to monitor the index of refraction of the sample—that is, I measure the nonlinear phase shift written by a signal pulse on this probe beam—and direct detection is used to isolate the effect of a single transmitted photon. For short pulses (10 ns, to be compared to the 26 ns atomic lifetime) and an optically thick medium (peak OD = 4, leading to 60% absorption given our broad bandwidth), I report that the average time atoms spend in the excited state due to one transmitted photon is not zero, but rather (77 +/- 16)% of the time the average incident photon causes them to spend in the excited state. This observation of “excitation without loss” is attributed to coherent forward emission, which arises, for instance, due to the sign-flip the instantaneous Rabi frequency (pulse envelope) picks up when a broadband pulse propagates through an optically thick medium with highly frequency-dependent absorption [1]. The results of this thesis reveal the complex history of photons as they propagate through an absorbing medium and illustrate the power of utilizing post-selection to experimentally investigate the past behaviour of observed quantum systems.
When a resonant photon traverses a sample of absorbing atoms, how much time do atoms spend in the excited state? Does the answer depend on whether the photon is ultimately scattered vs. transmitted? In particular, if it is not scattered, meaning that it emerges in the direction it entered, does it cause atoms to spend any time in the excited state, and if so, how much? In this thesis, I report an experimental measurement of the time a transmitted photon causes atoms to spend in the excited state. The experiment is carried out in an ultra-cold gas of Rubidium 85 atoms and involves simultaneously recording changes to the excited state occupation number induced by incident ("signal") photons and whether those photons are transmitted. The time atoms spend in the excited state, which is defined in terms of the time integral of the average excited state occupation number, is measured weakly using a separate, off-resonant “probe” laser to monitor the index of refraction of the sample—that is, I measure the nonlinear phase shift written by a signal pulse on this probe beam—and direct detection is used to isolate the effect of a single transmitted photon. For short pulses (10 ns, to be compared to the 26 ns atomic lifetime) and an optically thick medium (peak OD = 4, leading to 60% absorption given our broad bandwidth), I report that the average time atoms spend in the excited state due to one transmitted photon is not zero, but rather (77 +/- 16)% of the time the average incident photon causes them to spend in the excited state. This observation of “excitation without loss” is attributed to coherent forward emission, which arises, for instance, due to the sign-flip the instantaneous Rabi frequency (pulse envelope) picks up when a broadband pulse propagates through an optically thick medium with highly frequency-dependent absorption [1]. The results of this thesis reveal the complex history of photons as they propagate through an absorbing medium and illustrate the power of utilizing post-selection to experimentally investigate the past behaviour of observed quantum systems.
When a resonant photon traverses a sample of absorbing atoms, how much time do atoms spend in the excited state?Does the answer depend on whether the photon is ultimately absorbed or transmitted?In particular, if it is not absorbed, does it cause atoms to spend any time in the excited state and if so, how much?To answer these questions, we perform an experiment with ultracold rubidium atoms in which we simultaneously record whether atoms are excited by incident ("signal") photons and whether those photons are transmitted.We measure the time spent by atoms in the excited state by using a separate off-resonant "probe" laser to monitor the index of refraction of the sample-that is, we measure the nonlinear phase shift written by a signal pulse on this probe beam-and use direct detection to isolate the effect of single transmitted photons.For short pulses (10 ns, to be compared to the 26-ns atomic lifetime) and an optically thick medium (peak optical depth equals 4, leading to 60% absorption given our broad bandwidth), we find that the average time atoms spend in the excited state due to one transmitted photon is not zero but, rather, (77 ± 16)% of the time the average incident photon causes them to spend in the excited state.We attribute this observation of "excitation without loss" to coherent forward emission, which can arise when the instantaneous Rabi frequency (pulse envelope) picks up a 180 • phase flip-this happens naturally when a broadband pulse propagates through an optically thick medium with frequency-dependent absorption.These results unambiguously reveal for the first time the complex history of photons as they propagate through an absorbing medium and illustrate the power of utilizing postselection to experimentally investigate the past behavior of observed quantum systems.
When a resonant photon traverses a sample of absorbing atoms, how much time do atoms spend in the excited state? Does the answer depend on whether the photon is ultimately absorbed or transmitted? In particular, if it is not absorbed, does it cause atoms to spend any time in the excited state, and if so, how much? In an experiment with ultra-cold Rubidium atoms, we simultaneously record whether atoms are excited by incident ("signal") photons and whether those photons are transmitted. We measure the time spent by atoms in the excited state by using a separate, off-resonant "probe" laser to monitor the index of refraction of the sample - that is, we measure the nonlinear phase shift written by a signal pulse on this probe beam - and use direct detection to isolate the effect of single transmitted photons. For short pulses (10 ns, to be compared to the 26 ns atomic lifetime) and an optically thick medium (peak OD = 4, leading to 60% absorption given our broad bandwidth), we find that the average time atoms spend in the excited state due to one transmitted photon is not zero, but rather (77 ± 16)% of the time the average incident photon causes them to spend in the excited state. We attribute this observation of "excitation without loss" to coherent forward emission, which can arise when the instantaneous Rabi frequency (pulse envelope) picks up a phase flip - this happens naturally when a broadband pulse propagates through an optically thick medium with frequency-dependent absorption [1]. These results unambiguously reveal the complex history of photons as they propagate through an absorbing medium and illustrate the power of utilizing post-selection to experimentally investigate the past behaviour of observed quantum systems.
When a photon traverses a cloud of atoms without scattering, how much time does it spend as an atomic excitation? To address this question, we used the cross-Kerr effect to weakly probe the degree of atomic excitation caused by a transmitted resonant "signal" photon by measuring the phase shift induced on a (separate, off-resonant) "probe" beam, postselected on cases when the signal photon is transmitted. The time integral of this observed phase shift, properly normalized and averaged over many runs in which the photon is detected after transmission, is the excitation time of interest, in a weak-valued sense. We measured mean atomic excitation times ranging from (-0.82±0.31)τ_{0} for the most narrow band pulse to (0.54±0.28)τ_{0} for the most broadband signal pulse, where τ_{0} is the non-post-selected excitation time, given by the scattering probability multiplied by the atomic lifetime τ_{sp}. Across a range of pulse durations and optical depths, our results are consistent with the recent theoretical prediction that the weak value of the atomic excitation time caused by a transmitted photon equals the group delay experienced by the light. Our experimental results show that negative times are not limited to describing the shift in the peak of a reshaped wave packet (as resulting from group delay), but they also provide the appropriate description of the weak-valued time the photon spends as an atomic excitation.
When a single photon propagates through a cloud of two-level atoms, part of its energy is temporarily stored as a collective atomic excitation. This raises a fundamental question: is it possible to meaningfully quantify how long the photon spends in the form of an atomic excitation? If so, does this duration depend on whether the photon is ultimately transmitted through the cloud or scattered by the atoms? These questions motivated recent experimental work by some of us [Sinclair et al., PRX Quantum 3, 010314 (2022)], but until now there has been no theoretical prediction for these conditional durations. We answer these questions by extending the concept of a dwell time from quantum tunneling to light–matter interactions, introducing an experimentally measurable “atomic excitation time.” Using the weak-value formalism combined with quantum trajectory theory, we derive analytical expressions for this time conditioned on the photon being transmitted through the cloud or scattered into a side mode. We show that, for transmitted photons, this time is equal to the (spectrally averaged) group delay, even in regimes where the group delay is negative. For scattered photons, the time is given by the sum of an ensemble-averaged group delay and an always-positive Wigner time delay, well known in elastic scattering theory. Finally, we present a toy model that explains how such negative dwell times can arise as a result of quantum interference. This work provides new insight into the complex and surprising histories of photons traveling through absorptive media.
Under usual laboratory conditions the absorption of a beam of light by a dilute two-level medium depends on the intensity and spectrum of the incident light. If the incident photon flux is small compared to the decay rate of the absorber’s excited state, saturation effects can be neglected and only the spectrum of the light is important; thus, weak-field absorption depends only on the firstorder correlation function of the incident light. This result relies, however, on a requirement that the incident beam cross-section be much larger than the absorption cross-section of an atom. Then individual atoms act as low efficiency scatterers and the statistics of the scattering process is governed by the law of large numbers applied to many scattering sites. In contrast, if it is arranged that just one atom significantly absorbs (scatters) a beam of photons, correlation functions of the incident light beyond the first-order must be considered. For a beam that is focused within an absorption cross-section, we might naively predict that every photon will be scattered and none transmitted. In fact, even for a very weak beam there is a finite probability for two photons to arrive at the atom within the excited state lifetime, and in this event at least one of them will be transmitted (statistical saturation). In this paper we calculate the transmitted photon flux for a weak beam of photons focussed strongly onto a single, resonant two-state atom. We study the dependence of the transmitted flux on the statistics of the incident photons. Photon beams derived from sources of coherent, chaotic, squeezed, coherent-antibunched, and broadband-antibunched light are considered. our calculations are based on a recently developed theory of cascaded open systems,1,2 and serve to illustrate the usefulness of this theory.
This thesis deals with the study of propagation effects experienced by weak light pulses as they propagate in atomic media driven by strong pulses. We explore both the ultra-short and long pulse regime and investigate the phenomena that arise at these different time scales. In the short pulse regime, a strongly driven two level atomic system presents transient light shifts, and non-adiabatic transitions occur between these adiabatic levels. We have studied a method to probe these light shifts in real time by propagating a weak probe through the medium. The light shifts enrich the spectrum of the probe and the probe gets shaped as a result. In this way a strongly driven two-level system can act as an active pulse shaper, and can introduce oscillations in the temporal profile of an ultra-short pulse at a time scale shorter than the pulse duration. We also show that by driving the system with two time delayed non-resonant strong fields, the non-adiabatic effects can be rendered phase dependent. This gives very sensitive phase control of the excited state population and can be used to formulate new techniques in interferometry. In the long pulse regime we present a new method of slowing light that can be realized in a double two-level system interacting with two orthogonally polarized light pulses that propagate along different axis. Spatio-temporal dependence of the total polarization induces a grating in the ground Zeeman coherence. The stronger of the two fields (the control field) is diffracted from this grating into the direction of the weak probe field compensating for the absorption of this latter field. A transparency window is thus created in the absorption spectrum of the probe leading to the slowing down of light. The transparency window exhibits characteristics similar to the one obtained by EIT (electromagnetic induced transparency) method. However, the important difference between our method and the traditional EIT method, is that ours doesn't rely on realizing dark state in the system. This may open the possibility of slowing down light in more complex atomic media. Moreover, when the linear absorptive response of the medium is cancelled in this manner, the nonlinear response becomes more important. In the situation where fields propagate in the same direction and have same frequency, two regimes have been investigated. For small optical depths, the effective susceptibility behaves as chi_lin exp[2 i phi] (with phi the phase difference between two fields). This renders phase control of the medium response, and the medium can be changed from an absorber to an amplifier, with normal or anomalous dispersion, by adjusting the relative phase phi. In the regime of large optical thickness, phase saturation takes place and the effective susceptibility turns into chi_lin*, changing an absorber into an amplifier without effecting the dispersive response (chi_lin is linear susceptibility).