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

Journal of Optics

Nil-potent vacuum in homodyne noise

Ninad R. Jetty

Published Jan 5, 2022• 0 citations
Publisher

Abstract

Abstract In the absence of a signal field, vacuum entering through the empty beam splitter port is considered to be the sole contributor to the output noise of conventional two-port homodyne detection. We study a modified configuration that alters the input coefficient of vacuum, predicting an output noise less than that of the conventional configuration. Measurements, however, reveal identical output noise profiles for both the configurations. We explain the observations in terms of the incident field noise alone, and suggest that vacuum does not contribute to homodyne noise or shot-noise. We extend our results to the measurement of squeezed light, with non-ideal detectors.

DOI
10.1088/2040-8986/ac4871

Related papers

Noise in homodyne detection

Bonny L. Schumaker

A simple but rigorous analysis of the important sources of noise in homodyne detection is presented. Output noise and signal-to-noise ratios are compared for direct detection, conventional (one-port) homodyning, and two-port homodyning, in which one monitors both output ports of a 50-50 beam splitter. It is shown that two-port homodyning is insensitive to local-oscillator quadrature-phase noise and hence provides (1) a means of detecting reduced quadrature-phase fluctuations (squeezing) that is perhaps more practical than one-port homodyning and (2) an output signal-to-noise ratio that can be a modest to significant improvement over that of one-port homodyning and direct detection.

Optics Letters•May 1, 1984•244 citations

Squeezing more out of a laser

Carlton M. Caves

Machida and Yamamoto used negative feedback from a conventional photodetector to stabilize a laser's intensity and thus to obtain sub-shot-noise photon statistics within the feedback loop. Out-of-Ioop light extracted at a beam splitter, however, displayed super-shot-noise statistics. This behavior can be understood both quantum mechanically and semiclassically. Quantum mechanically the culprit is the vacuum field that enters the beam splitter’s second input port. I describe a technique for extracting sub-shot-noise light by replacing the culprit vacuum field with squeezed light generated by a nonlinear device—a squeezer—that is pumped by a portion of the laser light. Moreover, even if the unstabilized laser is shot-noise-limited, the extracted light can have a better intensity SNR; this signal-to-noise improvement requires both feedback and squeezing.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Reduction of quantum noise in optical interferometers using squeezed light

Michael Weyrauch, Volodymyr G. Voronov

We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so-called “dark port case,” when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (“dark port”). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R. Barak and Y. Ben-Aryeh, J. Opt. Soc. Am. B 25 , 361 (2008)]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.

arXiv:1010.5062•Optics and Spectroscopy•Nov 1, 2011•2 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

Fundamental limits to observations of squeezing via balanced homodyne detection

Samuel L. Braunstein, David D. Crouch

A photodetector's electronic bandwidth is the frequency range over which beats between different frequencies in the input can be observed in the output. The output of a balanced homodyne detector, the prototypical device for detecting squeezed light, consists of beats between a signal to be measured and a local oscillator. Beats between the signal and quantum local-oscillator fluctuations lead to noise that degrades the observed squeezing. Through wide-band calculations, we show that this noise contains contributions from the entire signal bandwidth, even when this bandwidth is orders of magnitude larger than the detector's electronic bandwidth. This allows us to place an upper limit on the total power that can enter the detector's signal port (both signal and extraneous light) within the detector's optical bandwidth in order for a given level of squeezing to be observable.

Physical Review A•Jan 1, 1991•10 citations

Quantum Noise in Balanced Differential Measurements in Optics: Implication to the Wave Modes of Quantum Vacuum

C. S. Unnikrishnan

Experimental tests for assessing the physical reality of the hypothetical wave modes of quantum vacuum with zero-point energy are of fundamental importance for quantum field theories and cosmology. Physical effects like the Casimir effect have alternate description in terms of retarded interaction between charged matter, due to quantum fluctuations of material dipoles. However, there are simple quantum optical configurations where the hypothetical quantum vacuum modes seem to assume an essential real role in the observable quantum noise of optical signals. I present the logical and theoretical basis of a decisive test that relies on the comparisons of balanced homodyne detection with a novel differential scheme of balanced wave-front division detection, when the two real optical beams at the detectors are derived from one coherent beam as input. Both ideal and practical configurations of my experimental test are discussed. Results from the experiments on balanced detection, beam localization of optical beams, and atomic Bose-Einstein condensates are used to reach definite conclusions against the reality of the wave modes of quantum vacuum. It is shown that the entire quantum noise follows consistently from the state reduction of quantum superpositions of particle-number states at the point of detection, where the quantum measurement is completed. This is consistent with the demonstrated applications of squeezed light in interferometry and quantum metrology. This result achieves consistency between quantum noise in quantum optics and observational cosmology based on general relativity, by avoiding the wave modes of quantum vacuum with divergent zero-point energy density. Generalization from the limited sphere of quantum optics to general quantum field theories promises the complete solution to the problem of a divergent cosmological constant.

arXiv:1912.11362•Dec 23, 2019•1 citation
Abstract In the absence of a signal field, vacuum entering through the empty beam splitter port is considered to be the sole contributor to the output noise of conventional two-port homodyne detection. We study a modified configuration that alters the input coefficient of vacuum, predicting an output noise less than that of the conventional configuration. Measurements, however, reveal identical output noise profiles for both the configurations. We explain the observations in terms of the incident field noise alone, and suggest that vacuum does not contribute to homodyne noise or shot-noise. We extend our results to the measurement of squeezed light, with non-ideal detectors.
A simple but rigorous analysis of the important sources of noise in homodyne detection is presented. Output noise and signal-to-noise ratios are compared for direct detection, conventional (one-port) homodyning, and two-port homodyning, in which one monitors both output ports of a 50-50 beam splitter. It is shown that two-port homodyning is insensitive to local-oscillator quadrature-phase noise and hence provides (1) a means of detecting reduced quadrature-phase fluctuations (squeezing) that is perhaps more practical than one-port homodyning and (2) an output signal-to-noise ratio that can be a modest to significant improvement over that of one-port homodyning and direct detection.
Machida and Yamamoto used negative feedback from a conventional photodetector to stabilize a laser's intensity and thus to obtain sub-shot-noise photon statistics within the feedback loop. Out-of-Ioop light extracted at a beam splitter, however, displayed super-shot-noise statistics. This behavior can be understood both quantum mechanically and semiclassically. Quantum mechanically the culprit is the vacuum field that enters the beam splitter’s second input port. I describe a technique for extracting sub-shot-noise light by replacing the culprit vacuum field with squeezed light generated by a nonlinear device—a squeezer—that is pumped by a portion of the laser light. Moreover, even if the unstabilized laser is shot-noise-limited, the extracted light can have a better intensity SNR; this signal-to-noise improvement requires both feedback and squeezing.
We study the photon counting noise in optical interferometers used for gravitational wave detection. In order to reduce quantum noise a squeezed vacuum state is injected into the usually unused input port. Here, we specifically investigate the so-called “dark port case,” when the beam splitter is oriented close to 90° to the incoming laser beam, such that nearly all photons go to one output port of the interferometer, and only a small fraction of photons is seen in the other port (“dark port”). For this case it had been suggested that signal amplification is possible without concurrent noise amplification [R. Barak and Y. Ben-Aryeh, J. Opt. Soc. Am. B 25 , 361 (2008)]. We show that by injection of a squeezed vacuum state into the second input port, counting noise is reduced for large values of the squeezing factor, however the signal is not amplified. Signal strength only depends on the intensity of the laser beam.
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.
A photodetector's electronic bandwidth is the frequency range over which beats between different frequencies in the input can be observed in the output. The output of a balanced homodyne detector, the prototypical device for detecting squeezed light, consists of beats between a signal to be measured and a local oscillator. Beats between the signal and quantum local-oscillator fluctuations lead to noise that degrades the observed squeezing. Through wide-band calculations, we show that this noise contains contributions from the entire signal bandwidth, even when this bandwidth is orders of magnitude larger than the detector's electronic bandwidth. This allows us to place an upper limit on the total power that can enter the detector's signal port (both signal and extraneous light) within the detector's optical bandwidth in order for a given level of squeezing to be observable.
Experimental tests for assessing the physical reality of the hypothetical wave modes of quantum vacuum with zero-point energy are of fundamental importance for quantum field theories and cosmology. Physical effects like the Casimir effect have alternate description in terms of retarded interaction between charged matter, due to quantum fluctuations of material dipoles. However, there are simple quantum optical configurations where the hypothetical quantum vacuum modes seem to assume an essential real role in the observable quantum noise of optical signals. I present the logical and theoretical basis of a decisive test that relies on the comparisons of balanced homodyne detection with a novel differential scheme of balanced wave-front division detection, when the two real optical beams at the detectors are derived from one coherent beam as input. Both ideal and practical configurations of my experimental test are discussed. Results from the experiments on balanced detection, beam localization of optical beams, and atomic Bose-Einstein condensates are used to reach definite conclusions against the reality of the wave modes of quantum vacuum. It is shown that the entire quantum noise follows consistently from the state reduction of quantum superpositions of particle-number states at the point of detection, where the quantum measurement is completed. This is consistent with the demonstrated applications of squeezed light in interferometry and quantum metrology. This result achieves consistency between quantum noise in quantum optics and observational cosmology based on general relativity, by avoiding the wave modes of quantum vacuum with divergent zero-point energy density. Generalization from the limited sphere of quantum optics to general quantum field theories promises the complete solution to the problem of a divergent cosmological constant.