Spectral broadening and shaping of nanosecond pulses: toward shaping of single photons from quantum emitters

Abstract

We experimentally demonstrate spectral broadening and shaping of exponentially-decaying nanosecond pulses via nonlinear mixing with a phase-modulated pump in a periodically-poled lithium niobate (PPLN) waveguide. A strong, 1550 nm pulse is imprinted with a temporal phase and used to upconvert a weak 980 nm pulse to 600 nm while simultaneously broadening the spectrum to that of a Lorentzian pulse up to 10 times shorter. While the current experimental demonstration is for spectral shaping, we also provide a numerical study showing the feasibility of subsequent spectral phase correction to achieve temporal compression and re-shaping of a 1 ns mono-exponentially decaying pulse to a 250 ps Lorentzian, which would constitute a complete spectro-temporal waveform shaping protocol. This method, which uses quantum frequency conversion in PPLN with > 100 : 1 signal-to-noise ratio, is compatible with single photon states of light. IntroductionHybrid quantum networks that combine different physical systems are one approach to achieving the varied functions needed in photonic quantum information processing systems [1]. Unfortunately, the disparate components of such a quantum network may not share the same spectro-temporal properties, leading to an intrinsic incompatibility that can only be overcome via an "adaptation interface." For example, single photon sources based on single quantum emitters like InAs quantum dots [2], nitrogen vacancy centers in diamond [3], and neutral alkali atoms [4] exhibit desirable features such as on-demand generation with the potential for high single photon purity. To interface the emission wavelengths below 1000 nm with the low-loss telecommunications band, quantum frequency conversion interfaces [5,6] have been proposed and developed, both in bulk and on-chip geometries. However, wavelength incompatibility is not the only challenge that needs to be overcome. While the temporal waveform of such two-level quantum emitters is typically a few nanosecond mono-exponential decay, telecommunications networks are better suited to Gaussian and square pulses that are much shorter in duration. Moreover, the bandwidth of quantum memories that are an integral part of the quantum repeater protocol may be either broader or narrower than the bandwidth of the photons [7]. Spectro-temporal shaping of single photons, while preserving their quantum nature, is thus a vital tool for hybrid quantum networks [8,9].

Quantum state and mode profile tomography by the overlap

“…To realize the scheme in practice, it is necessary to devise a way to change the overlap to produce the set of values, j b {¯}, sufficient for the inference. This can be achieved by shaping the spectral profile of the mode (see, for example, [11][12][13][14][15][16][17][18]). However, one really does not need to manipulate precisely a shape of the probe pulse to obtain the necessary set; a simple time-delay arrangement is sufficient (see section 3 for details).…”

“…where  denotes the normal ordering of the creation and annihilation operators. For example, to calculate the probability of no clicks at detector 1, p 1 (η 1 ), we set η 2 =0 in equation (16), that is p 1 (η 1 )=P(η 1 , 0). To compute the probabilities from the family of P(η 1 , η 2 ) in equation (16), we use the following identity I H H I H a a a a exp exp det , 1 7 1 where  denotes the antinormal ordering of the creation and annihilation operators and H is some positive semi-definite Hermitian matrix with eigenvalues bounded by 1.…”

“…Equation (17) can be verified by diagonalizing the matrix H, performing the series expansion of the exponents and checking the equality of both sides using the Fock states. In equation (16) we can identify the matrix H and find its inverse as:…”

“…In this sense, it may be considered as a diagnostic tool for existing tomographic reconstructions schemes, where identifying the modes is crucial to measuring the whole state [10]. Several techniques have been shown to shape temporal mode profiles [11][12][13][14][15][16][17][18][30][31][32][33][34][35] and the method to infer a modal temporal profile has a considerable practical value.We demonstrate these techniques experimentally using heralded single and two-photon states in welldefined modes and coherent probe field. The suggested tomographic scheme is resource efficient, requiring a single on-off detector.…”

Programmable optical waveform reshaping on a picosecond timescale

“…By tailoring an optical frequency comb, we create a specific pump waveform which interacts with an input signal in a χ (2) medium to produce an output signal with the target temporal profile. needs to be compressed and reshaped into simpler pulse shapes [4,5,[8][9][10] including Gaussian pulses [11]. Another example of optical reshaping is the generation of parabolic pulses from Gaussian pulses [12,13].…”