Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Conference on Lasers and Electro-Optics

Mapping of local complex reflection coefficient variations using a scanning multi-port homodyne interferometer

H. Jeong, K. Cho

Published Jan 1, 2001• 0 citations
Publisher

Abstract

Summary form only given. We present a novel multi-port balanced homodyne interferometer scheme, that can simultaneously determine the quadrature phases of the signal beam. This interferometer consists of two identical balanced homodyne interferometers, in which the local oscillators of the corresponding interferometers, have /spl pi//2 phase difference with respect to each other. In this scheme, two identical interferometers for quadrature measurements are constructed by the use of the corresponding polarization components of the signal and local oscillator beams, i.e., principal polarizations of the signal and local oscillator beams are used as independent interferometers. A /spl pi//4 phase shift between the reflected and transmitted polarization components at a polarizing beamsplitter, which was observed in our experiment, was used to provide two local oscillators with /spl pi//2 phase difference. Output interference signals from the corresponding. balanced interferometers, I and Q, respectively, can be written as, I=/spl eta/|E/sub LO/|E/sub s/| cos(/spl Delta//spl phi/),Q=/spl eta/|E/sub LO/|E/sub s/|sin(/spl Delta//spl phi/), where /spl eta/ is the quantum efficiency of photodiode, |E/sub s/| and |E/sub LO/| are the amplitude of signal and local oscillator beam, respectively, and /spl Delta//spl phi/ is the phase difference between signal and local oscillator.

DOI
10.1109/cleo.2001.947816

Related papers

Quantum State Characterization Using Measurement Configurations Inspired by Homodyne Detection

Arik Avagyan

In the standard homodyne configuration, an unknown optical state is combined with a local oscillator (LO) on a beam splitter (BS). Good quadrature measurements require a high-amplitude LO and two high-efficiency photodiodes whose signals are subtracted and normalized. By changing the LO phase, it is then possible to infer the optical state in the mode matching the LO. For quantum information processing, the states of interest are in well-separated modes, corresponding to a pulsed configuration with one relevant LO mode per measurement. We theoretically investigate what can be learned about the unknown optical state by counting photons in one or both outgoing paths after the BS, keeping the LO mode fixed but choosing its phase and magnitude. We consider measurement configurations where the BS acts differently on different sets of matching modes. When the BS acts identically on all matching modes it is possible to determine the content of the unknown optical state in the mode matching the LO conditional on each number of photons in the orthogonal modes on the same path. In particular, if both the phase and the intensity of the LO can be varied, then the statistics of just one of the counters is enough to infer these parameters, while in the case of an LO with fixed intensity both detectors are needed to accomplish this. Our results are derived by demonstrating a bijection, or lack thereof, between the probability distributions over the space of outcomes of the counter(s) and certain parameters of the unknown state for different measurement configuration. We report an experiment that was conducted to demonstrate the theory in the case where the BS acts differently depending on the polarization.

arXiv:2305.19397•May 30, 2023•1 citation

Polarization-based balanced heterodyne detection method in a Sagnac interferometer for precision phase measurement

Ke-Xun Sun, Eric K. Gustafson, M. M. Fejer +1 more

We describe a balanced heterodyne detection method for a Sagnac interferometer that uses a polarization-dependent beam splitter. The signal and the local oscillator are orthogonally polarized components of a single laser beam, permitting the detection of the signal by subtraction of two photocurrents produced in appropriate polarization projections. Using this scheme, we experimentally demonstrate a phase measurement with a sensitivity of 9x10(-10) rad/ radicalHz. The measurement is robust in the presence of laser frequency noise, as a result of preserving the common-path nature of the Sagnac interferometer, and of laser-amplitude noise, as a result of balanced detection.

Optics Letters•Sep 1, 1997•31 citations

Homodyne-like detection scheme based on photon-number-resolving detectors

Alessia Allevi, Matteo Bina, Stefano Olivares +1 more

Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.

International Journal of Quantum Information•Dec 1, 2017•13 citations

Double balanced homodyne detection

Kouji Nakamura, Masa‐Katsu Fujimoto

In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator $\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}$ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator $\hat{b}_θ$ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators $\hat{b}_{1}$ and $\hat{b}_{2}$ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator $\hat{b}_θ$ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.

arXiv:1711.03713•Nov 10, 2017•3 citations

Quantum security in homodyne reception using weak coherent states

E. García, Josué Aarón López-Leyva, Francisco Javier Mendieta +1 more

We present an experimental 8-port Balanced Homodyne Detector at 1550 nm wavelength, operating in free space, implemented with polarization devices to produce a circularly polarized local oscillator, splitting its In-Phase and Quadrature components to beat separately with the weak coherent incoming signal. This allows the simultaneous measurements of the 2 quadratures at the price of an additional noise due to the vacuum fields that leak via the unused ports, resulting in a modified Husimi function for joint probability distribution for the quadrature components. These schemes require the proper optical phase synchronization between the local oscillator and the incoming field, which constitutes a challenge for weak coherent state reception. To achieve this we designed and implemented an optical Costas loop; the feedback loop (especially the loop filter) which is a result of the optimal design has an impact on the mutual information between transmitter and receiver, being this parameter a condition to generate the cryptographic key. We present experimental and theoretical results on the performance of the mutual information between the transmitter and the receiver due the phase error for different photon numbers.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 10, 2011•1 citation

Homodyne statistics

Samuel L. Braunstein

It is usually assumed that a balanced homodyne detector measures a variable called the quadrature phase amplitude of a signal field. We examine this assumption by obtaining analytic expressions for the probability statistics for the output of such a detector for a single-mode signal with both signal and local oscillator treated quantum mechanically. We investigate the conditions under which the statistics of the quadrature phase are reproduced in the actual output of the detector. We show that the most obvious condition---that the number of quanta in the local oscillator be much larger than the number in the signal---is not sufficient to ensure that a balanced homodyne detector acts like an ideal detector of quadrature phases. Furthermore, we obtain the explicit conditions that are necessary and sufficient to reproduce the interference features in the homodyne statistics of a superposition of coherent states.

Physical Review A•Jul 1, 1990•80 citations
Summary form only given. We present a novel multi-port balanced homodyne interferometer scheme, that can simultaneously determine the quadrature phases of the signal beam. This interferometer consists of two identical balanced homodyne interferometers, in which the local oscillators of the corresponding interferometers, have /spl pi//2 phase difference with respect to each other. In this scheme, two identical interferometers for quadrature measurements are constructed by the use of the corresponding polarization components of the signal and local oscillator beams, i.e., principal polarizations of the signal and local oscillator beams are used as independent interferometers. A /spl pi//4 phase shift between the reflected and transmitted polarization components at a polarizing beamsplitter, which was observed in our experiment, was used to provide two local oscillators with /spl pi//2 phase difference. Output interference signals from the corresponding. balanced interferometers, I and Q, respectively, can be written as, I=/spl eta/|E/sub LO/|E/sub s/| cos(/spl Delta//spl phi/),Q=/spl eta/|E/sub LO/|E/sub s/|sin(/spl Delta//spl phi/), where /spl eta/ is the quantum efficiency of photodiode, |E/sub s/| and |E/sub LO/| are the amplitude of signal and local oscillator beam, respectively, and /spl Delta//spl phi/ is the phase difference between signal and local oscillator.
In the standard homodyne configuration, an unknown optical state is combined with a local oscillator (LO) on a beam splitter (BS). Good quadrature measurements require a high-amplitude LO and two high-efficiency photodiodes whose signals are subtracted and normalized. By changing the LO phase, it is then possible to infer the optical state in the mode matching the LO. For quantum information processing, the states of interest are in well-separated modes, corresponding to a pulsed configuration with one relevant LO mode per measurement. We theoretically investigate what can be learned about the unknown optical state by counting photons in one or both outgoing paths after the BS, keeping the LO mode fixed but choosing its phase and magnitude. We consider measurement configurations where the BS acts differently on different sets of matching modes. When the BS acts identically on all matching modes it is possible to determine the content of the unknown optical state in the mode matching the LO conditional on each number of photons in the orthogonal modes on the same path. In particular, if both the phase and the intensity of the LO can be varied, then the statistics of just one of the counters is enough to infer these parameters, while in the case of an LO with fixed intensity both detectors are needed to accomplish this. Our results are derived by demonstrating a bijection, or lack thereof, between the probability distributions over the space of outcomes of the counter(s) and certain parameters of the unknown state for different measurement configuration. We report an experiment that was conducted to demonstrate the theory in the case where the BS acts differently depending on the polarization.
We describe a balanced heterodyne detection method for a Sagnac interferometer that uses a polarization-dependent beam splitter. The signal and the local oscillator are orthogonally polarized components of a single laser beam, permitting the detection of the signal by subtraction of two photocurrents produced in appropriate polarization projections. Using this scheme, we experimentally demonstrate a phase measurement with a sensitivity of 9x10(-10) rad/ radicalHz. The measurement is robust in the presence of laser frequency noise, as a result of preserving the common-path nature of the Sagnac interferometer, and of laser-amplitude noise, as a result of balanced detection.
Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator b^θ:=cos⁡θb^1+sin⁡θb^2\hat{b}_θ:=\cosθ\hat{b}_{1}+\sinθ\hat{b}_{2}b^θ​:=cosθb^1​+sinθb^2​ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator b^θ\hat{b}_θb^θ​ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators b^1\hat{b}_{1}b^1​ and b^2\hat{b}_{2}b^2​ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator b^θ\hat{b}_θb^θ​ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.
We present an experimental 8-port Balanced Homodyne Detector at 1550 nm wavelength, operating in free space, implemented with polarization devices to produce a circularly polarized local oscillator, splitting its In-Phase and Quadrature components to beat separately with the weak coherent incoming signal. This allows the simultaneous measurements of the 2 quadratures at the price of an additional noise due to the vacuum fields that leak via the unused ports, resulting in a modified Husimi function for joint probability distribution for the quadrature components. These schemes require the proper optical phase synchronization between the local oscillator and the incoming field, which constitutes a challenge for weak coherent state reception. To achieve this we designed and implemented an optical Costas loop; the feedback loop (especially the loop filter) which is a result of the optimal design has an impact on the mutual information between transmitter and receiver, being this parameter a condition to generate the cryptographic key. We present experimental and theoretical results on the performance of the mutual information between the transmitter and the receiver due the phase error for different photon numbers.
It is usually assumed that a balanced homodyne detector measures a variable called the quadrature phase amplitude of a signal field. We examine this assumption by obtaining analytic expressions for the probability statistics for the output of such a detector for a single-mode signal with both signal and local oscillator treated quantum mechanically. We investigate the conditions under which the statistics of the quadrature phase are reproduced in the actual output of the detector. We show that the most obvious condition---that the number of quanta in the local oscillator be much larger than the number in the signal---is not sufficient to ensure that a balanced homodyne detector acts like an ideal detector of quadrature phases. Furthermore, we obtain the explicit conditions that are necessary and sufficient to reproduce the interference features in the homodyne statistics of a superposition of coherent states.