We propose a novel method for measuring the multitemporal mode quantum state of repetitive radiation fields with ultrafast temporal resolution. The technique incorporates spectrometers at the output ports of a DC-balanced four-port apparatus. The signal field to be measured is delayed in time with respect to an ultrashort local oscillator pulse which is taken to be in a large-amplitude single temporal mode coherent state. A quantum-mechanical analysis shows that the Fourier transform of the spectrally resolved difference counts is proportional to the multitemporal mode Q -function describing the signal field statistics. We apply the technique to reconstruct the multitemporal mode Q -function from simulated data of repetitive broadband chaotic light from which we calculate the photon number correlations between pairs of temporal modes.
We propose a novel method for measuring the multitemporal mode quantum state of repetitive radiation fields with ultrafast temporal resolution. The technique incorporates spectrometers at the output ports of a DC-balanced four-port apparatus. The signal field to be measured is delayed in time with respect to an ultrashort local oscillator pulse which is taken to be in a large-amplitude single temporal mode coherent state. A quantum-mechanical analysis shows that the Fourier transform of the spectrally resolved difference counts is proportional to the multitemporal mode Q -function describing the signal field statistics. We apply the technique to reconstruct the multitemporal mode Q -function from simulated data of repetitive broadband chaotic light from which we calculate the photon number correlations between pairs of temporal modes.
The technique of dc-balanced, pulsed homodyne detection for the purpose of determining optical-field statistics on short time scales is analyzed theoretically. Such measurements provide photon-number and phase distributions associated with a repetitive signal light field in a short time window. Time- and space-varying signal and local-oscillator pulses are treated, thus generalizing earlier treatments of photoelectron difference statistics in homodyne detection. Experimental issues, such as the effects of imperfect detector balancing on (time-integrated) dc detection and the consequences of background noise caused by non-mode-matched parts of the multimode signal field, are analyzed. The Wigner, or joint, distribution for the two field-quadrature amplitudes during the sampling time window can be directly determined by tomographic inversion of the measured photoelectron distributions. It is pointed out that homodyne detection provides a new method for the simultaneous measurement of temporal and spectral information. Although the theory is generally formulated, with both signal and local-oscillator fields being quantized, emphasis is placed on the limit of a strong, coherent local-oscillator field, making semiclassical interpretation possible.
We have measured the joint Q-function of a highly multimode field using unbalanced heterodyne detection with a charge-coupled device array detector. We use spectral interferometry between a weak signal field and a strong, 100 fs duration local oscillator pulse to reconstruct the joint quadrature amplitude statistics of about 25 temporal modes. By adjusting the time delay between the signal and local oscillator pulses we are able to shift all the classical noise to modes distinct from the signal. This obviates the need to use a balanced detector.
Abstract Recent progress in ultrafast optics facilitates the investigation of the dynamics of highly multimode quantum states of light. Yet, the complete tomographic reconstruction of optical quantum states with prior unknown statistics and dynamics is still challenging, since state-of-the-art tomographic methods require the measurement of orthogonal and distinguishable modes. Here, we propose a tomography scheme based on time-domain quadrature correlation measurements and theoretically demonstrate its ability to reconstruct highly multimode Gaussian states. In contrast to (eight-port) homodyne detection, the two local oscillator pulses are shorter in time and are (independently) time-delayed against the pulsed quantum state. The distinguishable mode structure is obtained in post-processing from the correlation measurement data by orthogonalization. We show that the number of reconstructable modes increases with the number of time delays used and decreases with the temporal extent of the local oscillator. Additionally, we compare dual-pulse homodyne detection and electro-optic sampling. By analysing the (quantum) correlations present in the measurement data, we show how thermalisation of the quantum state during detection leads to the requirement of correlation measurements. Furthermore, we open an avenue to extending our tomography scheme to non-Gaussian states.
Ultimately the properties of all optical fields are contained in the density matrix that specifies their quantum mechanical state. It has only recently been demonstrated that it is possible to actually reconstruct this density matrix from measured data, and to do so with temporal resolution of a few hundred femtoseconds.[1] This technique, known as Optical Homodyne Tomography (OHT), is unfortunately restricted to the measurement of only single mode radiation. In fact it selects out from the test field only those components which overlap temporally with the local oscillator pulse mode.
A photon is the single excitation of a particular spatiotemporal mode of the electromagnetic field. A precise knowledge of the mode structure is therefore essential for its processing and detection, as well as for applying generic quantum light states to novel technologies. Here we demonstrate an adaptive scheme for reconstructing the arbitrary amplitude and phase spectro-temporal profile of an ultrashort single-photon pulse. The method combines techniques from the fields of ultrafast coherent control and quantum optics to map the mode of a fragile quantum state onto that of an intense coherent field. In addition, we show that the possibility of generating and detecting quantum states in multiple spectro-temporal modes may serve as a basis for encoding qubits (and qudits) into single, broadband, ultrashort, photons. Providing access to a much larger Hilbert space, this scheme may boost the capacity of current quantum information protocols.
Quantum physics holds promise to revolutionise a number of technologies by enabling performance beyond what is feasible with classical resources, such as secure communications, precision measurement and high-speed simulation and computation. To realise this, quantum information must be encoded into one of the physical degrees of freedom of light. The time-frequency (TF) domain provides a infinite-dimensional space which is naturally compatible with integrated optical platforms. Additionally, future quantum networks will require coherent coupling of quantum systems that do not necessarily exhibit TF mode overlap. The ability to generate, coherently control and measure a variety of TF states of quantum light is therefore a necessary step towards implementing optical quantum technologies. Developing the building blocks for future optical quantum applications calls for an assortment of methods for measuring the properties of TF states of quantum light. Whilst much progress has been made towards this goal recently, deficiencies with existing methods remain. Efficient spectrally-resolved detection away from the telecoms wavelength range and a robust approach to single-photon state characterisation that is sensitive to the spectral phase have so far proven challenging. Additionally, accessing quantum advantages requires measurements that are sensitive to the nonclassical correlations that can exist between separate subsystems. However, until now a flexible approach to determining the full quantum state of systems of multiple time/frequency entangled photons has been lacking. Here we develop a toolbox of techniques for the measurement of TF quantum states of light for few-photon systems, and apply these to the task of precision measurement. Firstly, we propose, construct and demonstrate efficient single-photon spectrometers based on dispersive time-to-frequency mapping, using chirped fibre Bragg gratings to apply the necessary group delay dispersion. We use two such devices operating in coincidence to realise a full phase-sensitive reconstruction of the TF state of a single photon, by spectrally resolving the output of a nonclassical interference process with an external reference. We also demonstrate a complementary, optical reference-free method. This characterisation tool, an implementation of electro-optic spectral shearing interferometry with coincident spectrally-resolved single-photon detection, melds techniques from ultrafast metrology and quantum optics. We proceed to demonstrate the flexibility of this device by reconstructing a wide range of test pulses generated with a pulse shaper. By implementing this technique in conjunction with spectrally-resolved detection of a second photon, we realise complete characterisation of the TF wave function of a spectrally-entangled broadband photon pair. This method is robust to a wide range of inputs and is generalisable to spectrally mixed states and across a wide range of wavelengths, including to spectrally non-degenerate photon pairs. To demonstrate, we generate an entangled photon pair with controllable TF entanglement and perform a full reconstruction. Lastly, we present a new technique for using TF entangled photon pairs to realise quantum-enhanced measurement of a time delay in a quantum channel in the presence of environmental noise. This scheme is based on entanglement-enhanced rejection of background light. A simple experiment demonstrating the feasibility of such a measurement is presented.