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arXiv:1910.03848 · Physical Review A

Efficient generation of temporally shaped photons using nonlocal spectral filtering

Valentin Averchenko, Сыч Денис Васильевич, Christoph Marquardt, Gerd Leuchs

Published Jan 10, 2020• 23 citations
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Abstract

We study the generation of single-photon pulses with the tailored temporal shape via nonlocal spectral filtering. A shaped photon is heralded from a time-energy entangled photon pair upon spectral filtering and time-resolved detection of its entangled counterpart. We show that the temporal shape of the heralded photon is defined by the time-inverted impulse response of the spectral filter and does not depend on the heralding instant. Thus one can avoid postselection of particular heralding instants and achieve a substantially higher heralding rate of shaped photons as compared to the generation of photons via nonlocal temporal modulation. Furthermore, the method can be used to generate shaped photons with a coherence time in the ns-$\ensuremath{\mu}\mathrm{s}$ range and is particularly suitable to produce photons with the exponentially rising temporal shape required for efficient interfacing to a single quantum emitter in free space.

DOI
10.1103/physreva.101.013808

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We study the generation of single-photon pulses with the tailored temporal shape via nonlocal spectral filtering. A shaped photon is heralded from a time-energy entangled photon pair upon spectral filtering and time-resolved detection of its entangled counterpart. We show that the temporal shape of the heralded photon is defined by the time-inverted impulse response of the spectral filter and does not depend on the heralding instant. Thus one can avoid postselection of particular heralding instants and achieve a substantially higher heralding rate of shaped photons as compared to the generation of photons via nonlocal temporal modulation. Furthermore, the method can be used to generate shaped photons with a coherence time in the ns-\ensuremathμs\ensuremath{\mu}\mathrm{s}\ensuremathμs range and is particularly suitable to produce photons with the exponentially rising temporal shape required for efficient interfacing to a single quantum emitter in free space.
We present a method to produce pure single photons with an arbitrary designed temporal shape in a heralded way. As an indispensable resource, the method uses pairs of time-energy entangled photons. One photon of a pair undergoes temporal amplitude-phase modulation according to the desired shape. Subsequent frequency-resolved detection of the modulated photon heralds its entangled counterpart in a pure quantum state. The temporal shape of the heralded photon is indirectly affected by the modulation in the heralding arm. We derive conditions for which the shape of the heralded photon is given by the modulation function. The method can be implemented with various sources of time-energy entangled photons. In particular, using entangled photons from parametric down-conversion the method provides a simple means to generate pure shaped photons with an unprecedented broad range of temporal durations, from tenths of femtoseconds to microseconds. This shaping of single photons will push forward the implementation of scalable multidimensional quantum information protocols, efficient photon-matter coupling, and quantum control at the level of single quanta.
We analyze the quantum-state purity of heralded single photons produced from frequency-anticorrelated biphotons. We find that the quantum-state purity in the time-frequency domain depends strongly on the response time uncertainty of the trigger-photon detector that heralds the generation of its paired photon. If the trigger response time is much shorter than the two-photon coherence time, the time-frequency quantum-state purity of heralded single photons approaches unity and the heralded single photon is in a nearly pure state. If the trigger response time is much longer than the two-photon coherence time, the heralded photon is then projected onto a mixed state. Making use of the time-frequency entanglement, heralded single photons with a well-defined temporal wave function or a frequency superposition state can be produced and engineered. This time-frequency entanglement allows for shaping heralded single photons through nonlocal spectral modulation.
We experimentally demonstrate temporal shaping of a heralded single-photon wave packet, prepared by conditional measurement of the idler photon of the entangled photon pair in the process of spontaneous parametric down-conversion. The heralded single-photon wave packet for the signal photon, after being tailored with the help of chirp broadening and interference effects, was observed directly by measuring the time-correlated single-photon-counting histogram. We also demonstrate remote control of the temporal shaping effect by spectral filtering of the idler photon.
We present an experimental and theoretical analysis of the energy-time entanglement properties of a two-photon state generated by pulsed spontaneous parametric down-conversion. Different methods of spectral or temporal shaping of one of the two photons have allowed the observation of nonlocal modulations in the autocorrelation or in the spectrum of the other, by coincidence measurements. Either a monochromator or etalon filters have been used to shape the idler photon while observing the conditioned signal autocorrelation with a Michelson interferometer. Alternatively, the unbalanced interferometer has been used to shape the signal photon while measuring the conditioned idler spectrum with the monochromator. The role of the pump spectrum has been investigated by shaping it with additional filters. A theoretical treatment has allowed us to completely describe all the observed features as a function of the different experimental parameters.
A major obstacle to a practical, heralded source of single photons is the fundamental trade-off between high purity and high production rate. To overcome this difficulty, we propose applying sequential spectral and temporal filtering on the signal photons before they are detected for heralding. Based on a multimode theory that takes into account the effect of simultaneous multiple photon-pair emission, we find that these filters can be optimized to yield both high purity and a high production rate. While the optimization conditions vary depending on the underlying photon-pair spectral correlations, all correlation profiles can lead to similarly high performance levels when optimized filters are employed. This suggests that a better strategy for improving the performance of heralded single-photon sources is to adopt an appropriate measurement scheme for the signal photons, rather than tailoring the properties of the photon-pair generation medium.
Nonlocal shaping effects in the time or spectral profiles of an entangled photon pair emerging from a pulsed parametric down-converter are observed by spectrally or temporally filtering one of the twin beams. In particular, we demonstrate the appearance of fourth-order ("ghost") interference fringes in the spectrum of one beam conditioned by photodetection at the output of an unbalanced Michelson interferometer placed in the path of the other beam. The coherence time of the pump is the limiting factor for the sharpness of the details in the shaped biphoton spectrum.