Destructive interference between opposite time orders of photon emission

Schrama, C. A.; Nienhuis, G.; Dijkerman, H.A.; Steijsiger, C.; Heideman, H G M

doi:10.1103/physrevlett.67.2443

Cited by 31 publications

(28 citation statements)

References 8 publications

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“…For a similar reason, the correlation between two photons from opposite sidebands displays bunching, since the first emission puts the atom in the dressed state where the second emission starts. The correlation functions in this case take the form [16] for a=F or T. The relations (5.8), which follow from (2.12), show that the amplitude for successive emission of an R photon and a photon from one of the sidebands is just the opposite of the amplitude for the twofold emission in the opposite order [3]. If we substitute (5.8) and 5=0; dotted line: 5=A, /4; dashed line: 5=X/2.…”

Section: B Short-time Behaviormentioning

confidence: 91%

“…The Rabi frequency 0 measures the strength of the atom-field coupling, and A=cocoo is the detuning of the which leads to complete antibunching [3]. For two photons from opposite sidebands, the correlation function also displays a dip at zero time delay, which exactly counterbalances the photon bunching on the longer time scale of the inverse linewidths [4].…”

Section: Fluorescence Tripletmentioning

confidence: 99%

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Spectral correlations in resonance fluorescence

Nienhuis

1993

Phys. Rev. A

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We study the photon correlations between the output of two spectral filters set within the fluorescence triplet of a two-state atom. The time uncertainty arising from the spectral resolution of the filters implies a possible interference between opposite orders of emission, contributing to the same detection order. Furthermore, the fluorescent emission is a quantum-mechanical process, and successive emissions in different components do not commute. The correlation functions are affected both by the memory time of the filters and by the noncommutativity of successive emissions. When the two filter bandwidths are larger than the widths of the components, this only modifies the short-time behavior of the correlation functions between two photons from different spectral components. For narrow filters, the entire correlation function is dominated by memory-time effects. Positive (bunching) correlations arise when the two filters are set at the same frequency, and also when they are positioned symmetrically at opposite sides of the driving frequency.PACS number(s): 42.50.Dv 32.80.t

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Section: B Short-time Behaviormentioning

confidence: 91%

Section: Fluorescence Tripletmentioning

confidence: 99%

Spectral correlations in resonance fluorescence

Nienhuis

1993

Phys. Rev. A

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“…To our knowledge, no other experiments investigating phase-dependent fluorescence spectra have produced data of high enough quality for detailed 0031-9007͞97͞79(4)͞613(4)$10.00 comparison with theory [8][9][10]. Using frequency filtered resonance fluorescence, it has been possible to observe temporal correlations between sideband photons [11] and interference between different time orderings of Rayleigh and sideband photons [12].…”

Section: Phase-dependent Resonance Fluorescence and Time Ordering In mentioning

confidence: 99%

Phase-Dependent Resonance Fluorescence and Time Ordering in Photodetection

Zhao

Thomas

1997

Phys. Rev. Lett.

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We measure phase-dependent fluorescence spectra of two-level atoms driven by a monochromatic laser field, for off-resonance excitation. Pairs of spectra with phases of opposite sign are found to display striking differences that arise entirely from time ordering.[S0031-9007 (97)03685-5] PACS numbers: 32.80. -t, 42.50.LcTime ordering arises naturally in quantum mechanics and is explicit in the well known Dyson expansion for the time translation operator [1]. Physically, time ordering enforces causality in the measurement process: a measurement at time t can affect the quantum state and hence the possible outcomes of future measurements at times t 0 . t. In photodetection, this has the consequence that the intensity correlation functions that correctly describe measurements of optical fields at multiple times must be both normal and time ordered [2]. Thus, it is possible to view time ordering in quantum optics as a consequence of the photodetection process. Alternatively, time ordering in photodetection can be viewed as a consequence of fluctuations in the vacuum field [3,4]. In this picture, vacuum fluctuations provide a formal description of photons, leading to shot noise and atom-field interactions that are discrete in time.In this Letter, we show that phase-dependent resonance fluorescence spectra dramatically exhibit the consequences of time ordering in the detection of photons from atomic systems. Phase-dependent resonance fluorescence spectra are obtained by homodyne detection of scattered radiation from free atoms that are irradiated by a quasiresonant field. The radiation field E of the atoms is mixed with a local oscillator (LO) field jE LO je if having a controllable fixed phase f relative to the field that drives the atoms. The interference between the LO and atom radiation fields then leads to fluctuations in the detected power that are determined by the quadrature operatorThe spectrum of the detected power fluctuations is measured with a spectrum analyzer for different LO phases f. We find that quadrature spectra for phases of f 645 ± are strikingly different when the driving field is offresonance, and we show that this difference is entirely due to time ordering. The phase-dependent power spectrum (with the shot noise of the LO removed) is the Fourier transform of the correlation function C f ͑t͒ ͗:x f ͑t 2 ͒x f ͑t 1 ͒:͘, where t 2 t 1 1 t and : : denotes normal ordering. The angled brackets denote a quantum statistical average and a time average over t 1 . Two types of two-time field correlation functions appear in C f ͑t͒. The first are of the form ͗Ê y ͑t 2 ͒Ê ͑t 1 ͒͘ 1 c.c. which are phase independent. Here, the time ordering is determined by the normal ordering. These lead to ordinary resonance fluorescence spectra. Of particular interest are the phase-dependent terms of the form e 22if ͗Ê ͑t 2 ͒Ê ͑t 1 ͒͘ 1 c.c. Here, the time ordering is not determined by normal ordering.The field operatorÊ ͑t͒ can be considered to contain both a source field (atom) contributionÊ S and a free vacuum fieldÊ V . ...

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“…In particular, under certain conditions it may reverse the time order of two photons, in that the photon that was emitted earlier may be detected later. In such a case, destructive interference between two opposite time orders of emitting a pair of photons may substantially reduce the joint probability of detecting both photons at the same time, in principle all the way down to zero [2,3]. Moreover, the filtering process may change the photon statistics from antibunched to bunched [4].…”

Section: Introductionmentioning

confidence: 99%

“…It turns out then that the frequency filtering operation can play an active and nontrivial role in the detection of two-photon correlations [2][3][4]. In particular, under certain conditions it may reverse the time order of two photons, in that the photon that was emitted earlier may be detected later.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent spectrum of a single photon and its positive-operator-valued measure

Enk

2017

Phys. Rev. A

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Suppose we measure the time-dependent spectrum of a single photon. That is, we first send the photon through a set of frequency filters (which we assume to have different filter frequencies but the same finite bandwidth Γ), and then record at what time (with some finite precision ∆t, and with some finite efficiency η) and after passing what filter the photon is detected. What is the POVM (PositiveOperator Valued Measure, the most general description of a quantum measurement) corresponding to such a measurement? We show how to construct the POVM in various cases, with special interest in the case Γ∆t 1 (time-frequency uncertainty still holds, even in that limit). One application of the formalism is to heralding single photons. We also find a Hong-Ou-Mandel type of interference effect with two photons entering a frequency filter.

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Destructive interference between opposite time orders of photon emission

Cited by 31 publications

References 8 publications

Spectral correlations in resonance fluorescence

Spectral correlations in resonance fluorescence

Phase-Dependent Resonance Fluorescence and Time Ordering in Photodetection

Time-dependent spectrum of a single photon and its positive-operator-valued measure

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