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Physical Review A

Reconstruction of a multimode entangled state using a two-photon phase-sensitive linear amplifier

Mashhood Ahmad, Shahid Qamar, Muhammad Suhail Zubairy

Published Apr 23, 2003• 11 citations
Publisher

Abstract

We propose a model for the measurement of an arbitrary multimode entangled state of the cavity field using two-photon correlated emission laser. We consider two cases: (a) The modes have different frequencies and are detected separately and (b) the modes consist of two orthogonal polarization states and are detected using a single balanced homodyne detector. The basic idea is to amplify the initial multimode state such that there is no-noise in the quadrature of interest and all the noise is fed into the conjugate quadrature component. The amplified noise-free quadrature is prepared in different phases and then corresponding quadrature distribution is measured. The Wigner function of the initial multimode entangled state is then reconstructed by using inverse Radon transformation. This scheme is insensitive to the noise associated with the nonunit efficiency of the detector in the homodyne detection measurement scheme.

DOI
10.1103/physreva.67.043815

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We propose a model for the measurement of an arbitrary multimode entangled state of the cavity field using two-photon correlated emission laser. We consider two cases: (a) The modes have different frequencies and are detected separately and (b) the modes consist of two orthogonal polarization states and are detected using a single balanced homodyne detector. The basic idea is to amplify the initial multimode state such that there is no-noise in the quadrature of interest and all the noise is fed into the conjugate quadrature component. The amplified noise-free quadrature is prepared in different phases and then corresponding quadrature distribution is measured. The Wigner function of the initial multimode entangled state is then reconstructed by using inverse Radon transformation. This scheme is insensitive to the noise associated with the nonunit efficiency of the detector in the homodyne detection measurement scheme.
We propose a model for the quantum-state measurement via phase-sensitive amplification. The basic idea is to amplify the quantum state through a two-photon correlated-emission laser, such that there is no noise in the quadrature of interest and all the noise is fed into the conjugate quadrature. The noise-free quadrature is prepared in different phases and then corresponding quadrature distribution is measured. The Wigner function of the initial quantum state is then reconstructed by carrying out inverse Radon transformation familiar in tomographic imaging. This scheme allows us to avoid the deterioration of homodyne detection measurement due to the problem of detector efficiency.
Balanced homodyne detection relies on a beam splitter to superpose the weak signal input and strong local oscillator. However, recent investigation shows that a high gain phase sensitive amplifier (PSA) can be viewed as homodyne detector, in which the strong pump of PSA serves as the local oscillator [1]. Here, we analyze a new method of measuring the continuous variable entanglement by assisting a balanced homodyne detector with the PSA and implement it experimentally. Before measuring quadrature amplitude with the balanced homodyne detectors, two entangled fields generated from a pulse pumped fiber optical parametric amplifier are simultaneously coupled into the PSA. We find that the normalized noise for both the difference and sum of the quadrature amplitudes of the two entangled fields fall below the shot noise limit by about 4.6 dB, which is the record degree of entanglement measured in optical fiber systems. The experimental results illustrate that the advantages of the new measurement method include but not limit to tolerance to detection loss and characterizing entanglement with only one homodyne detector. The influence of mode-mismatching due to multi-mode property of entanglement on the measured noise reduction can also be greatly mitigated, indicating the new method is advantageous over the traditional measurement in multi-mode case.
We propose schemes for measuring the joint quantum state of a two-mode optical field using balanced homodyne detection, thereby generalizing earlier single-mode schemes. We distinguish between two cases---the case where the two modes are spatially separable and the case where they are nonseparable. For each case we present a generalization of the direct sampling method of state reconstruction and point out that its advantages over inverse Radon methods are even greater here than in the single-mode case. In the case of two modes that cannot be separated we propose a scheme in which a single balanced homodyne detector is used for data collection. \textcopyright{} 1996 The American Physical Society.
The traditional method for measuring Einstein-Podolsky-Rosen-type continuous-variable quantum entanglement relies on balanced homodyne detections, which are sensitive to vacuum quantum noise coupled in through losses due to various factors such as detector quantum efficiency and mode mismatching between the detected field and the local oscillator. In this paper, we propose and analyze a measurement method, which is realized by assisting the balanced homodyne detections with a high-gain phase-sensitive parametric amplifier. The employment of the phase-sensitive amplifier helps us to tackle the vacuum quantum noise originating from detection losses. Moreover, because the high-gain phase-sensitive amplifier can couple two fields of different types, the proposed scheme can be used to reveal quantum entanglement between two fields of different types by using only one balanced homodyne detection. Furthermore, detailed analysis shows that in the multimode case, the proposed scheme is also advantageous over the traditional method. Such a measurement method should find wide applications in quantum information and quantum metrology involving measurement of continuous variables.
Phase-sensitive amplification in a three-level atomic system exhibits interesting features. For example, in the zero-detuning limit and for sufficiently strong driving field, this system becomes an ideal parametric amplifier, whereas, for a weak driving field it is a phase-insensitive amplifier [Ansari et al., Phys. Rev. A 41, 5179 (1990)]. In this paper, we show that this system could be used to measure the quantum state of the radiation field inside a cavity. To reconstruct the quantum state, we amplify it through a three-level atomic system and in the parametric limit, when noise in both the quadratures approaches to zero measure the amplified field quadrature. The complete quadrature distribution is obtained by measuring the quadratures for different values of the driving field phases. The inverse Radon transformation is then employed to reconstruct the original quantum state. Our scheme is insensitive to the problems associated with nonunit detector efficiency in homodyne detection measurement.
Phase-controlled homodyne 2(N+R)-port detection with R local oscillators is analyzed with the aim of reconstructing the quantum state of a correlated N-mode signal field. It is shown that both the (N+R)-fold joint count distributions and the N-fold joint difference-count distributions contain all knowable information on the state of the field. In any case, the minimum number of local oscillators is given by the number of different signal-field frequencies. Two Fourier integrals per mode are found to be required to reconstruct the density matrix of the signal field from the joint difference-count distributions measured in balanced homodyning. To illustrate the theory, it is applied to balanced homodyne 4N-port detection (R=N). In this scheme, the joint difference-count distributions directly yield the joint field-strength distributions of a correlated N-mode signal field.