Abstract Single photons are very useful resources in quantum information science. In real applications it is often required that the photons have a well-defined spectral (or equivalently temporal) modal structure. For example, a rising exponential pulse is able to fully excite a two-level atom while a Gaussian pulse cannot. This motivates the study of continuous-mode single-photon Fock states. Such states are characterized by a spectral (or temporal) pulse shape. In this paper we investigate the statistical property of continuous-mode single-photon Fock states. Instead of the commonly used normal ordering (Wick order), the tool we proposed is the Wigner spectrum. The Wigner spectrum has two advantages: (1) it allows to study continuous-mode single-photon Fock states in the time domain and frequency domain simultaneously; (2) because it can deal with the Dirac delta function directly, it has the potential to provide more information than the normal ordering where the Dirac delta function is always discarded. We also show how various control methods in particular coherent feedback control can be used to manipulate the pulse shapes of continuous-mode single-photon Fock states.
Abstract Single photons are very useful resources in quantum information science. In real applications it is often required that the photons have a well-defined spectral (or equivalently temporal) modal structure. For example, a rising exponential pulse is able to fully excite a two-level atom while a Gaussian pulse cannot. This motivates the study of continuous-mode single-photon Fock states. Such states are characterized by a spectral (or temporal) pulse shape. In this paper we investigate the statistical property of continuous-mode single-photon Fock states. Instead of the commonly used normal ordering (Wick order), the tool we proposed is the Wigner spectrum. The Wigner spectrum has two advantages: (1) it allows to study continuous-mode single-photon Fock states in the time domain and frequency domain simultaneously; (2) because it can deal with the Dirac delta function directly, it has the potential to provide more information than the normal ordering where the Dirac delta function is always discarded. We also show how various control methods in particular coherent feedback control can be used to manipulate the pulse shapes of continuous-mode single-photon Fock states.
Creating and controlling well-defined single-photon states is important for many quantum enhanced technologies. Information can be encoded in any degree of freedom associated with a single-photon field excitation, for example in the polarization or transverse spatial mode structure. The ability to encode multiple qubits in these states is desirable for high data transmission rates and increased information processing capacity. The spectral-temporal domain offers a large Hilbert space for encoding information, well suited to integrated optical architectures owing to the low cross-talk between channels. Indeed, time-frequency encoding is an integral component of existing information technologies infrastructure. Thus, complete, coherent control of the spectral-temporal mode structure of light is essential to advancing optical quantum technologies. Arbitrary control of single-photon states has been demonstrated in the polarization and spatial-momentum degrees of freedom however, is yet to be established in the spectral-temporal domain. Recently it was shown that spectral-temporal pulse shaping is experimentally feasible using nonlinear optical methods. However, such techniques can introduce noise photons, are challenging to implement deterministically and require specially prepared auxiliary pump pulses. Furthermore, they are typically only possible at relatively low repetition rates to avoid damage of nonlinear optical materials. Here, we demonstrate deterministic pulse shaping of single-photon wave packets by introducing a time-varying phase. Applying linear or quadratic phase to the wave packet introduces a spectral shift or spectral broadening, respectively. Achieving significant spectral manipulation requires temporal-phase modulation on the order of π. The phase must also vary on the same time scale as the optical pulses, approximately 1 ps in duration here. This relatively rapid phase variation is achieved using a fast electro-optic phase modulator. The modulator is driven by a time-varying voltage that is synchronized with a pulse train of single-photon wave packets for accurate temporal phase control. In this thesis, we experimentally demonstrate control of the spectral-temporal state of single-photon wave packets using this method. Heralded single-photon wave packets are generated by spontaneous parametric down conversion pumped by a frequency-doubled Titanium-Sapphire laser oscillator with 80 MHz repetition rate. To achieve significant modulation of single-photon pulses a 10 V peak-to-peak radio-frequency signal of 40 GHz drives the phase modulator, which requires approximately 3.6 V to achieve a π phase shift. The signal is synchronized with the oscillator pulse train using custom designed electronics. Details of these electronics are presented, resulting in a robust phase and amplitude controllable 40 GHz voltage source, phase locked to the single-photon pulse train. To demonstrate the utility of this pulse-shaping method we experimentally show spectral shearing of almost 1 nm for single-photon wave packets with 830 nm central wavelength and 1 nm bandwidth. Measurement of the second-order intensity correlation before and after the wave-packet manipulation remains constant within uncertainty of the measurement, showing that the quantum nature of the single-photon source is not deteriorated by the modulator. Preservation of the wave-packet coherence is verified by two-photon interference between spectrally sheared and non-modulated single-photons.
In this survey, we first introduce quantum fields and open quantum systems, then we present continuous-mode single-photon states and discuss discrete measurements of a single-photon field. After that, we introduce linear quantum systems and show how a linear quantum system responds to a single-photon input. Then we investigate how a coherent feedback network can be used to manipulate the temporal pulse shape of a single-photon state. Afterwards, we present single-photon filter and master equations. Finally, we discuss the generation of Schrödinger cat states by means of photon addition and subtraction
The ability to control the temporal shape of single-photon pulses is highly desirable in quantum information processing. For instance, it has been shown that Gaussian pulses are best suited for linear optics quantum computing1. By mimicking the time-reversal of a spontaneous emission event, it also allows to optimize the absorption of the prepared photons by a quantum emitter. In this work we investigate the potential of using fast modifications of the detuning between an atomic system and a cavity mode during photon emission to reach this goal. We compare two approaches consisting of varying the emitter or cavity frequency. The latter, achievable by a fast modification of the refractive index of a solid state cavity, will be shown to have negligible influence on the photon spectrum. It allows to create Gaussian pulses interacting with a fidelity to the target photons of 99%, as well as time-reversed photons absorbed by an atom in a cavity with a probability of 93%.
Temporal-spectral modes of light provide a fundamental window into the nature of quantum systems and offer a robust means for information encoding. Methods to precisely characterize the temporal-spectral state of light at the single-photon level thus play a central role in understanding single-photon sources and their applications in emerging optical quantum technologies. Here we demonstrate an optical reference-free method, which melds techniques from ultrafast metrology and single-photon spectral detection, to characterize the pulse-mode structure of heralded single photons.
Single photons provide a natural platform for quantum communication and quantum networking, as they can be entangled in many degrees of freedom and maintain coherence over long-distance links. However, while their minimal interactions with the environment isolate them from detrimental noise, it can make them difficult to measure and manipulate. In particular, manipulation on the ultrafast timescale is necessary to fully exploit the energy-time (or spectral) photonic degree of freedom. Full control over the spectral properties of single photons is key to many quantum technologies and opens the door to natural high-dimensional quantum encodings. \n \nIn this thesis, we theoretically and experimentally examine the use of nonlinear optical processes mediated by strong laser pulses as a method to control the spectral properties of ultrafast single photons. By mixing single-photon pulses with strong escort pulses that have been shaped through dispersion in a nonlinear crystal, the shape of the escort is imprinted on the photon, resulting in a custom-tailored upconverted pulse. We theoretically examine this process for quadratic spectral phases and show that it has the potential to be simultaneously effective and efficient for the customization of single-photon spectral waveforms, and can be performed in an entanglement-conserving manner. \n \nWe then experimentally demonstrate the range of this technique through three applications. First, we show that sum-frequency generation with shaped pulses can be used to coherently measure time-bin encoded photons with bin separations on the order of picoseconds, well below the timing resolution of our detectors. Secondly, we show that this technique can be adapted to convert a train of pulses to a frequency comb, which can be read out in a straightforward manner using diffraction-based spectrometry. We also show here that this process can be performed in a polarization-maintaining fashion, and demonstrate that entanglement with a partner photon is conserved with high fidelity. Finally, we show that this process can be viewed as a time lens, which modulates a temporal waveform in an analogous fashion to a lens focusing a beam of light. We apply the time lens to a photon from an energy-time entangled pair, and show negative magnification of the joint spectrum through a reversal of the spectral correlations. Such processes could find application in quantum state engineering and high-speed single-photon measurement.
Abstract Manipulation of quantum optical pulses, such as single photons or entangled photon pairs, enables numerous applications, from quantum communications and networking to enhanced sensing. Common methods to shape laser pulses based upon filtering or amplification cannot be employed with quantum light pulses as these approaches introduce detrimental loss and noise to the system. Here, methods to control and measure quantum light pulses based upon deterministic application of targeted phases in time and frequency domains are reviewed, along with recent demonstrations of quantum applications.