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Quantum Electronics and Laser Science Conference

Ultrafast time-resolved photon-number statistics

M. Munroe, Deepak Boggavarapu, Matthew E. Anderson, Michael G. Raymer

Published May 22, 1995• 0 citations
OpenAlex

Abstract

Optical homodyne tomography1 (OHT) has previously been used to determine the quantum state of fields,2 and thus the photon-number statistics3 of these fields in the 300-ps regime. We have demonstrated the use of OHT to measure the time-resolved photon-number statistics of a 5-ns pulsed field with a sampling time of 130 fs and time resolution of 60 ps. The ultrafast sampling allows us to measure the statistics of very-broadband fields, such as that of a diode laser below threshold.

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Optical homodyne tomography1 (OHT) has previously been used to determine the quantum state of fields,2 and thus the photon-number statistics3 of these fields in the 300-ps regime. We have demonstrated the use of OHT to measure the time-resolved photon-number statistics of a 5-ns pulsed field with a sampling time of 130 fs and time resolution of 60 ps. The ultrafast sampling allows us to measure the statistics of very-broadband fields, such as that of a diode laser below threshold.
We prove that the photon-number distribution of an arbitrary single-mode optical state can be calculated directly from the phase-averaged quadrature amplitude distribution, measured using optical homodyne detection. We experimentally demonstrate the application of this result by measuring the ultrafast (subpicosecond), time-resolved photon-number statistics of a weak field from a pulsed diode laser. Also presented is a numerical calculation of the photon-number distribution of a quadrature-squeezed vacuum state.
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.
Optical homodyne tomography (OHT) is a tool that allows the reconstruction of Wigner functions for each detection frequency of a propagating optical beam. It can measure probability distribution functions (PDF's) of the field amplitude for any given quadrature of interest. We demonstrate OHT for a range of classical optical states with constant and time varying modulations and show the advantage of OHT over conventional homodyne detection. The OHT simultaneously determines the signal to noise ratio in both amplitude and phase quadratures. We show that highly non-Gaussian Wigner functions can be obtained from incoherent superpositions of optical states.
Generation and measurement of quantum states of the electromagnetic field represent a hot and widely discussed topic in the Physics community, since optical states are useful not only in fundamental experiments but also in several applications in the fields of Quantum Optics and Quantum Information (Bouwmeester et al., 2000). In fact, optical radiation is endowed with relevant characteristics as it travels at maximum possible speed, it is almost unaffected by the interaction with the environment, which in many cases represents an unavoidable decoherence source, and it can be integrated in optoelectronic circuits to implement quantum computing protocols (Sansoni et al., 2010). The possibility of using optical fields in applicative protocols depends on the capability of generating and manipulating optical states that are robust with respect to losses (i.e. that contain a sizeable number of photons) and that can be produced and measured at high rate. For all these reasons, mesoscopic pulsed optical states containing few tens of photons per pulse seem to be the ideal candidates for applications to quantum communication protocols in which each pulse must be addressed individually. Moreover, the problem of generating suitable pulsed states must be considered together with the question of their measurement and characterization. In fact, nowadays we have many types of pulsed-light sources at our disposal, each of them characterized by different pulse durations (from few fs up to few ns), different pulse-repetition rates (from few Hz to 100 MHz) and a wide range of energies per pulse (from few nJ to several J). However, not all these pulsed light can be easily measured. In the mesoscopic intensity regime, for example, detectors endowed with photon-number resolution are required so as to determine shot-by-shot photon numbers or, at least, to characterize some features of the optical states. In fact, full characterization of the optical state, obtained e.g. by evaluating its Wigner function, can be achieved with optical homodyne tomography (OHT) (Raymer, 1997), a technique that over the years has proved its effectiveness in reconstructing both classical and quantum states, even if further optimizations are needed in the case of pulsed fields (Zavatta et al., 2006). Direct detection schemes are an alternative to OHT in all the cases in which knowing the statistics of detected photons is sufficient to characterize the signal state, as demonstrated in the pioneering work of Arecchi (Arecchi, 1965). Obviously, the implementation of a direct detection scheme requires a proper choice of the detector, the development of a calibration 11
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.