Efficient generation of temporally shaped photons using nonlocal spectral filtering

Valentin Averchenko, Denis Sych, Christoph Marquardt, and Gerd Leuchs

Phys. Rev. A 101, 013808 – Published 10 January 2020

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- $μ s$ 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.

Received 14 October 2019

DOI:https://doi.org/10.1103/PhysRevA.101.013808

Physics Subject Headings (PhySH)

Quantum entanglement Quantum optics

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Valentin Averchenko^1,*, Denis Sych^2,3,4, Christoph Marquardt^5,6, and Gerd Leuchs^5,6,7

¹St. Petersburg State University, Ul'yanovskaya street 3, 198504 Sankt-Peterburg, Russia
²P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskiy Prospekt 53, 119991 Moscow, Russia
³Russian Quantum Center, Skolkovo, 143025 Moscow, Russia
⁴Moscow Pedagogical State University, 29 Malaya Pirogovskaya St, 119435 Moscow, Russia
⁵Max-Planck-Institut for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
⁶Institute for Optics, Information and Photonics, University Erlangen-Nürnberg, Staudtstraße 7/B2, 91058 Erlangen, Germany
⁷Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov street, 603950 Nizhny Novgorod, Russia

^*valentin.averchenko@gmail.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 101, Iss. 1 — January 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Generation of temporally shaped single-photon pulses from time-energy entangled photon pairs via (a) nonlocal temporal modulation or (b) nonlocal spectral filtering. As an example, the generation of photons with the exponentially rising temporal shape is considered. Time-energy entangled photons are called signal and idler, for convenience. The photons are correlated in the time domain, i.e., their conditional temporal width $t_{c}$ is smaller than unconditional width $t_{u}$ : $t_{c} ≪ t_{u}$ . In (a) the idler photon is modulated with the exponentially rising waveform, with the characteristic modulation time $t_{m}$ . In (b) the idler photon passes the spectral filter with the Lorentzian transmission function with the characteristic bandwidth $ω_{m} \sim t_{m}^{- 1}$ . Inset shows the corresponding amplitude (solid line) and phase (dashed line) of the impulse response of the spectral filter. In the first case, postselection of the particular outcome of the frequency-resolving detector is required to herald a signal photon with the desired temporal shape and carrier frequency. The postselection is performed with a spectral resolution $ω_{d}$ . In the second case, the detection instant defines the timing of the heralded shaped photon. Characteristic temporal resolution of the detector is $t_{d}$ . All clicks herald signal photons with identical temporal shape and can be used without postselection.
Reuse & Permissions
Figure 2
Joint probability densities of entangled photons are represented by the blue ellipses in the frequency (left) and time (right) domains. $ω_{u}, t_{u}$ denote the unconditional spectral and temporal widths of signal or idler photons and $ω_{c}, t_{c}$ denote conditional ones. The ellipses tend to antidiagonal or diagonal lines in the limit of perfectly correlated photons. Spectral filtering of the idler photon and its successful time-resolved detection heralds a shaped signal photon such that its spectral shape is defined by the frequency-reversed transmission function of the filter [see (5)] and its temporal shape is defined by the time-reversed impulse response of the filter [see (6)].
Reuse & Permissions
Figure 3
(a) Temporal distribution of idler photons before (dashed line) and after (solid line) spectral filter in the idler arm. (b) Temporal distribution of signal photons conditioned upon detection of idler photons at time instants $t_{1}^{'}, t_{2}^{'}, t_{3}^{'}$ (solid curves). Dashed curves represent distributions obtained without spectral filtering of idler photons and reproduce a second-order cross-correlation function. The functions are normalized to unity at their maximum. The relation between parameters is chosen as follows: $t_{u} : t_{m} : t_{c} = 150 : 10 : 1$ . The heralding probability for these parameters is $R \approx 0.17$ according to (15).
Reuse & Permissions
Figure 4
Time-dependent probability $p (t)$ (solid blue line) of finding a two-level atom in the upper state upon free space mode-matched excitation of the atom with a single-photon resonant pulse with exponentially rising temporal shape $| ψ_{s} {(t) |}^{2}$ (gray dashed line) produced via nonlocal filtering [see (27)]. The parameters are chosen the same as in Fig. 3, i.e., $t_{m} : t_{c} = 10 : 1$ . Temporal shape of the photon is normalized to unity at the maximum. Maximum excitation probability for given parameters is $p_{max} = 0.95$ and it is achieved at $t = 0$ that is the heralding instant of the shaped photon.
Reuse & Permissions
Figure 5
Gray dashed line denote heralding probability (23) of photons with the exponentially rising temporal shape (25) as a function of $ɛ = t_{m} / t_{c}$ . Solid blue line denotes maximal excitation probability (29) of a two-level atom achieved via the full solid angle illumination with the single photon. The rise time of the exponential photon shape is matched to the radiative lifetime of the atomic transition.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information