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

A method of measuring the amplitude-modulated vacuum field near a conducting mirror

Sun-Hyun Youn, Jai-Hyung Lee, Joon-Sung Chang

Published May 1, 1994• 0 citations
OpenAlex

Abstract

Electromagnetic fields of the vacuum mode near a conducting mirror are modified with respect to those in free space, with their amplitudes having a sinusoidal spatial dependence from the mirror. Therefore if we combine this spatially amplitude-modulated vacuum field mode and intense coherent light with a beam splitter, we may detect this fluctuation of the vacuum mode in a homodyne detection scheme. It will give a new method to produce squeezed states of light with a single mirror placed close to an unused port of a beam splitter. We show that the amplitude fluctuation of the combined light can be reduced by a factor of 2 below that of the coherent light. We also discuss the limitations due to the finite line width of the laser and the effective absorption length of the photodiodes.

Related papers

Insightful Approach to Quantum Noise Suppression Below the Standard Quantum Limit Using a Single Mirror and Beam Splitter

Sun-Hyun Youn

When a coherent electromagnetic wave passes through a beam splitter (BS), it is divided equally into two parts. However, the quantum noise associated with the resulting coherent states, despite being reduced in amplitude by half, remains fundamentally constrained by the quantum noise limit, independent of the intensity. By placing a mirror at the unused input port of the BS, a standing wave is formed in the vicinity of the mirror, which influences the vacuum fluctuations of the coherent state at the BS output. Using semi-classical and quantum mechanical approaches, we calculate the vacuum fluctuations induced by the mirror and demonstrate that the vacuum noise originating from the mirror side periodically reaches zero at the BS output. Leveraging this effect, we show that the vacuum fluctuations of the light split by the BS can be readily reduced below the quantum noise limit. Furthermore, through feedback mechanisms, the vacuum fluctuations of the electromagnetic field at the other output port can also be suppressed below the quantum noise limit. These findings provide a pivotal insight into the manipulation of electromagnetic noise, with broad implications for all experiments involving quantum noise control.

arXiv:2506.08521•Jun 10, 2025•0 citations

Boundary-conditioned spatial redistribution of electric-field vacuum fluctuations in a mirror–beam-splitter system

Sun-Hyun Youn

We analyze electric-field vacuum fluctuations in a beam-splitter system with one port terminated by a mirror. The aim is not to propose passive generation of a squeezed quantum state, but to clarify how Maxwell boundary conditions modify the spatial mode function on which vacuum-field operators act. The mirror-side vacuum contribution acquires a standing-wave structure, so its local electric-field variance is suppressed at electric-field nodes and enhanced at antinodes. Throughout this work, the reference quantum noise level (QNL) means the local variance contributed by an unconstrained traveling-wave vacuum mode having the same spectral, polarization, transverse-mode, and field-normalization conventions as the mirror-conditioned mode. A “sub-QNL” statement therefore refers only to a specified local, mode-resolved electric-field contribution, and not to the total noise of an arbitrary detector or to a globally squeezed freely propagating state. Using semiclassical and quantum-operator descriptions, we derive the position-dependent variance at the beam-splitter outputs and show that the effect is local and mode-selective, rather than a nonlinear transformation of the quantum state. For an ideal point detector and a perfect standing wave, the position-dependent standing-wave component is suppressed by 100% at a node relative to its antinode value, although the total measured variance retains spatially uniform contributions from the remaining modes. We provide explicit suppression and signal-to-noise expressions and discuss their degradation by finite visibility and spatial averaging. We also discuss the conditions required for observing this redistribution and its relation to feedback-based noise reduction and the standard quantum limit.

Physics Letters A•Aug 17, 2026•0 citations

Quantum measurements with an amplitude-squeezed-light beam splitter

Junxiang Zhang, Tiancai Zhang, Ruifang Dong +3 more

Quantum measurement of amplitude fluctuation is performed by the injection of 2.5-dB amplitude-squeezed light produced by a quantum-well laser into the dark port of a beam splitter as the meter wave. It is shown that the measurements satisfy the criteria of quantum nondemolition measurement. The measured transfer coefficient and the quantum-state preparation ability are 1.07 and 0.8, respectively.

Applied Optics•Nov 10, 2001•4 citations

Pulsed squeezed vacuum measurements without homodyning

Jérôme Wenger, Jaromı́r Fiurášek, Rosa Tualle-Brouri +2 more

Following a recent theoretical proposal [J. Fiur\'a\ifmmode \check{s}\else \v{s}\fi{}ek and N. J. Cerf, Phys. Rev. Lett. 93, 063601 (2004)], we experimentally implement a scheme to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. The suggested setup is based on only a tunable beam splitter and a direct single-photon detector to fully characterize the generated Gaussian states. We discuss the experimental implementation of this procedure and compare it to other reference methods. A detailed exploitation of our results highlights some practical limitations of this method. This experimental work is followed by a detailed numerical analysis to derive the conditions required for the procedure to succeed. In particular, it is found that an overall single-photon detection efficiency of about 50% is needed, which is difficult to achieve in the present experiment.

arXiv:quant-ph/0403234•Physical Review A•Nov 11, 2004•44 citations

Vacuum state squeezing versus squeezed classical noise: a test using conditional homodyne detection

H. J. Carmichael

Measurement of the squeezed fluctuations of an optical field by the method of conditional homodyne detection is discussed. It is shown that conditional homodyne detection is able to distinguish qualitatively between vacuum-state squeezing and squeezed classical noise. Whereas for conventional squeezed-light detection, only a quantitative distinction can be made, based on the setting of the shot-noise level, under conditional detection, the presence of classical noise changes the actual shape of the measured correlation function. The correlations show a positive peak due to the unsqeezed classical noise frequencies, set inside the negative dip associated with the squeezed fluctuations. The width in time of the positive peak is the larger of the detector response time and the inverse of the classical noise bandwidth. The fundamental distinction between vacuum-state squeezing and squeezed classical noise is that there is no positive peak, even in the limiting form of a delta-function, when the unsqueezed frequencies correspond to vacuum state modes. Implications for the literal interpretation of vacuum fluctuations, such as is adopted in stochastic electrodynamics, are discussed. The ideas are presented in general terms and illustrated by an example which treats the generation and detection of broadband squeezed light, including finite-bandwidth classical noise, within the framework of the quantum trajectory theory of cascaded open systems.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 16, 2003•1 citation

Standard quantum limit of angular motion of a suspended mirror and homodyne detection of a ponderomotively squeezed vacuum field

Yutaro Enomoto, Koji Nagano, Seiji Kawamura

Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum back-action noise, or in other words the first-order vacuum field is ponderomotively squeezed. It is also shown that the Gouy phase shift the light acquires between the mirror and the position of detection of the light corresponds to the homodyne angle. Therefore, the quantum back-action noise can be canceled and the standard quantum limit can be surpassed by choosing the appropriate position of detection analogously to the cancellation of quantum radiation pressure noise by choosing an appropriate homodyne angle.

arXiv:1602.05344•Physical Review A•Jul 20, 2016•15 citations
Electromagnetic fields of the vacuum mode near a conducting mirror are modified with respect to those in free space, with their amplitudes having a sinusoidal spatial dependence from the mirror. Therefore if we combine this spatially amplitude-modulated vacuum field mode and intense coherent light with a beam splitter, we may detect this fluctuation of the vacuum mode in a homodyne detection scheme. It will give a new method to produce squeezed states of light with a single mirror placed close to an unused port of a beam splitter. We show that the amplitude fluctuation of the combined light can be reduced by a factor of 2 below that of the coherent light. We also discuss the limitations due to the finite line width of the laser and the effective absorption length of the photodiodes.
When a coherent electromagnetic wave passes through a beam splitter (BS), it is divided equally into two parts. However, the quantum noise associated with the resulting coherent states, despite being reduced in amplitude by half, remains fundamentally constrained by the quantum noise limit, independent of the intensity. By placing a mirror at the unused input port of the BS, a standing wave is formed in the vicinity of the mirror, which influences the vacuum fluctuations of the coherent state at the BS output. Using semi-classical and quantum mechanical approaches, we calculate the vacuum fluctuations induced by the mirror and demonstrate that the vacuum noise originating from the mirror side periodically reaches zero at the BS output. Leveraging this effect, we show that the vacuum fluctuations of the light split by the BS can be readily reduced below the quantum noise limit. Furthermore, through feedback mechanisms, the vacuum fluctuations of the electromagnetic field at the other output port can also be suppressed below the quantum noise limit. These findings provide a pivotal insight into the manipulation of electromagnetic noise, with broad implications for all experiments involving quantum noise control.
We analyze electric-field vacuum fluctuations in a beam-splitter system with one port terminated by a mirror. The aim is not to propose passive generation of a squeezed quantum state, but to clarify how Maxwell boundary conditions modify the spatial mode function on which vacuum-field operators act. The mirror-side vacuum contribution acquires a standing-wave structure, so its local electric-field variance is suppressed at electric-field nodes and enhanced at antinodes. Throughout this work, the reference quantum noise level (QNL) means the local variance contributed by an unconstrained traveling-wave vacuum mode having the same spectral, polarization, transverse-mode, and field-normalization conventions as the mirror-conditioned mode. A “sub-QNL” statement therefore refers only to a specified local, mode-resolved electric-field contribution, and not to the total noise of an arbitrary detector or to a globally squeezed freely propagating state. Using semiclassical and quantum-operator descriptions, we derive the position-dependent variance at the beam-splitter outputs and show that the effect is local and mode-selective, rather than a nonlinear transformation of the quantum state. For an ideal point detector and a perfect standing wave, the position-dependent standing-wave component is suppressed by 100% at a node relative to its antinode value, although the total measured variance retains spatially uniform contributions from the remaining modes. We provide explicit suppression and signal-to-noise expressions and discuss their degradation by finite visibility and spatial averaging. We also discuss the conditions required for observing this redistribution and its relation to feedback-based noise reduction and the standard quantum limit.
Following a recent theoretical proposal [J. Fiur\'a\ifmmode \check{s}\else \v{s}\fi{}ek and N. J. Cerf, Phys. Rev. Lett. 93, 063601 (2004)], we experimentally implement a scheme to measure the squeezing and purity of a single-mode squeezed vacuum state without an interferometric homodyne detection. The suggested setup is based on only a tunable beam splitter and a direct single-photon detector to fully characterize the generated Gaussian states. We discuss the experimental implementation of this procedure and compare it to other reference methods. A detailed exploitation of our results highlights some practical limitations of this method. This experimental work is followed by a detailed numerical analysis to derive the conditions required for the procedure to succeed. In particular, it is found that an overall single-photon detection efficiency of about 50% is needed, which is difficult to achieve in the present experiment.
Measurement of the squeezed fluctuations of an optical field by the method of conditional homodyne detection is discussed. It is shown that conditional homodyne detection is able to distinguish qualitatively between vacuum-state squeezing and squeezed classical noise. Whereas for conventional squeezed-light detection, only a quantitative distinction can be made, based on the setting of the shot-noise level, under conditional detection, the presence of classical noise changes the actual shape of the measured correlation function. The correlations show a positive peak due to the unsqeezed classical noise frequencies, set inside the negative dip associated with the squeezed fluctuations. The width in time of the positive peak is the larger of the detector response time and the inverse of the classical noise bandwidth. The fundamental distinction between vacuum-state squeezing and squeezed classical noise is that there is no positive peak, even in the limiting form of a delta-function, when the unsqueezed frequencies correspond to vacuum state modes. Implications for the literal interpretation of vacuum fluctuations, such as is adopted in stochastic electrodynamics, are discussed. The ideas are presented in general terms and illustrated by an example which treats the generation and detection of broadband squeezed light, including finite-bandwidth classical noise, within the framework of the quantum trajectory theory of cascaded open systems.
Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum back-action noise, or in other words the first-order vacuum field is ponderomotively squeezed. It is also shown that the Gouy phase shift the light acquires between the mirror and the position of detection of the light corresponds to the homodyne angle. Therefore, the quantum back-action noise can be canceled and the standard quantum limit can be surpassed by choosing the appropriate position of detection analogously to the cancellation of quantum radiation pressure noise by choosing an appropriate homodyne angle.