Accurate photonic temporal mode analysis with reduced resources

Abstract

The knowledge and thus characterization of the temporal modes of quantum light fields is important in many areas of quantum physics ranging from experimental setup diagnosis to fundamentalphysics investigations. Recent results showed how the auto-correlation function computed from continuous-wave homodyne measurements can be a powerful way to access the temporal mode structure. Here, we push forward this method by providing a deeper understanding and by showing how to extract the amplitude and phase of the temporal mode function with reduced experimental resources. Moreover, a quantitative analysis allows us to identify a regime of parameters where the method provides a trustworthy reconstruction, which we illustrate experimentally.PACS numbers: 42.50.Dv, Techniques to characterize quantum states have become more and more valuable with the development of quantum information science. In order to establish standards and check the compliance of the different building blocks, it is necessary to have efficient and reliable measurement methods. However, characterizing quantum states is challenging by nature [1]. One quantum measurement only provides a limited amount of information and therefore it is always necessary to perform multiple measurements to obtain a full quantum state characterization. All the art lies in the way of assembling those pieces of information [2,3].Beyond the conceptual interest, it is also important to pay attention to the practical aspects: Each measurement demands experimental resources, e.g., time, energy, money and processing power. Regarding the valuable character of the measurements, it is thus essential to know how the choice of the experimental parameters, on one hand, and the evaluation technique, on the other hand, can maximize the amount of extracted information. In other words, the question is how to obtain the desired characterization at reduced costs.Optical states constitute the essential ingredient of many quantum information protocols, for quantumnetwork applications [4,5] as well as all-optical processing [6]. Among the different degrees of freedom that define an optical mode, the temporal shape has lately arisen an increasing interest [7]. However, it appears to be challenging to control [8]. Although theoretical models have been developed for various systems [9, 10], they don't always accurately describe the experimental implementation. Hence, in order to verify, experimental techniques to measure the temporal mode are necessary. The Hong-Ou-Mandel experiment was probably the first technique looking closely at the characterization problem of temporal modes [11]. Although it gives information about the coherence of the temporal shape, this technique evaluates the degree of indistinguishability and does not provide any information about the details of a possible mismatch. In addition, it remains restricted to single-photon states.Recently new methods have been developed to tackle the challenge in practical cases [12][13][14][15][16][17][18]. Those techniques = ? ? + ? ? Unkno...

Deterministic Shaping and Reshaping of Single-Photon Temporal Wave Functions

“…we obtain from (31) arg(E out ) = arg(e) = arg(L) + arg(Ω) − Im(K)h(t) (33) that we can rewrite to arg(Ω) = arg(e) − arg(L) + Im(K)h(t) .…”

“…Here we provide details and discussions about the temporal mode measured with a homodyne detection [33].…”

“…Indeed, there is no way to determine which mode is f 1 and which one is f 2 . However, as explained in [33], this ambiguity can be lifted with an additional measurement with a detuned local oscillator. Nevertheless, in our case this ambiguity is not a relevant issue as we have a very good agreement between theory and experiment.…”

“…We moreover shape the photon phase, demonstrate the mode selectivity of photon absorption, and stretch and compress a given single-photon wave packet by 3 orders of magnitude. All these achievements are realized in combination with a convenientto-implement coherence-testing method that outputs the time-dependent complex-valued temporal mode function with minimal resources [33]. As both the amplitude and the phase of the temporal mode are determined with respect to a commonly accepted reference, a phase-locked laser, we are now in a position to certify the (absolute) coherence of a network photon.Our system uses the quantum memory scheme described in Ref.…”

“…In order to evaluate the temporal shape e(t) of the emitted photon, i.e. amplitude and phase, we use a temporal mode analysis technique [33,36,37]. As explained in the SM, from a set of homodyne measurements we obtain the real and imaginary part of the temporal mode function e(t).…”