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Physical Review A

Simultaneous quantum-state measurements using array detection

Andrew M. C. Dawes, M. Beck

Published Mar 19, 2001• 11 citations
Publisher

Abstract

We have simultaneously measured the quantum states of two different spatial modes of the same optical beam by performing quantum-state tomography with an array detector. Both modes are well described by coherent states, but the projection of the signal onto the local oscillator mode contains a mean of 0.09 photons, while a more complicated mode has a mean of 4.3 photons. This demonstrates that for this particular mode the effective detection efficiency when using array detection is over 40 times greater than when using single detectors.

DOI
10.1103/physreva.63.040101

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We have simultaneously measured the quantum states of two different spatial modes of the same optical beam by performing quantum-state tomography with an array detector. Both modes are well described by coherent states, but the projection of the signal onto the local oscillator mode contains a mean of 0.09 photons, while a more complicated mode has a mean of 4.3 photons. This demonstrates that for this particular mode the effective detection efficiency when using array detection is over 40 times greater than when using single detectors.
I propose a method for measuring the quantum state of an optical field that occupies a mode having a complicated spatial structure. The technique uses array detectors and a single, plane-wave local oscillator beam. The advantage of using array detectors is that the local oscillator is not mode matched to the field being measured, yet the deleterious effects of this mismatch on the effective detection efficiency are greatly reduced compared to using single detectors. Indeed, when the spatial mode of the signal field is describable by a real function, the effective mode-matching efficiency is unity.
We demonstrate that it is possible to choose an optimal signal mode for state reconstruction when performing quantum-state tomography with array detectors. The mode optimization is done during the data analysis (i.e., after all the data have been collected.) We develop theoretically a procedure for finding the mode that satisfies a criterion which is quadratic in field operators; as examples we explicitly show how to maximize the average photon number, or the amount of quadrature squeezing. We experimentally demonstrate the technique by finding the mode which maximizes the average photon number for coherent-state signal beams occupying both linear and sinusoidal modes.
We propose a method of resolving a spatially coherent signal, which contains on average just a single photon, against the background of local noise at the same frequency. The method is based on detecting the signal simultaneously in several points more than a wavelength apart through the entangling interaction of the incoming photon with the quantum metamaterial sensor array. The interaction produces the spatially correlated quantum state of the sensor array, characterised by a collective observable (e.g., total magnetic moment), which is read out using a quantum nondemolition measurement. We show that the effects of local noise (e.g., fluctuations affecting the elements of the array) are suppressed relative to the signal from the spatially coherent field of the incoming photon as , where N is the number of array elements. The realisation of this approach in the microwave range would be especially useful and is within the reach of current experimental techniques.
We demonstrate that it is possible to use the balanced homodyning with array detectors to measure the quantum state of a correlated two-mode signal field. We show the applicability of the method to fields with complex mode functions, thus generalizing the work of Beck [Phys. Rev. Lett. 84, 5748 (2000)] in several important ways. We further establish that, under suitable conditions, array detector measurements from one of the two ouputs are sufficient to determine the quantum state of signal. We show the power of the method by reconstructing a truncated Perelomov state, which exhibits complicated structure in the joint probability density for the quadratures.
The reconstruction of density matrices from measurement data (quantum state tomography) is the most comprehensive method for assessing the accuracy and performance of quantum devices. Existing methods to reconstruct two-photon density matrices require the detection of both photons unless a priori information is available. Based on the concept of quantum-induced coherence by path identity, we present an approach to quantum state tomography that circumvents the requirement of detecting both photons. We show that an arbitrary two-qubit density matrix, which can contain up to fifteen free parameters, can be fully reconstructed from single-photon measurement data without any postselection and a priori information. In addition to advancing an alternative approach to quantum state measurement problems, our results also have notable practical implications. A practical challenge in quantum state measurement arises from the fact that effective single-photon detectors are not readily accessible for a wide spectral range. Our method, which eliminates the need for coincidence measurements, enables quantum state tomography in the case where one of the two photons is challenging or impossible to detect. It therefore opens the door to measuring quantum states hitherto inaccessible.