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

Sun-Hyun Youn

TL;DR

By placing a mirror at the unused input port of a beam splitter, the authors engineer the spatial structure of vacuum modes and form a standing wave that modulates vacuum fluctuations at the outputs. Both semi-classical and quantum-operator analyses show that the standing-wave boundary condition creates nodes where vacuum noise vanishes (e.g., at $k z_1 = n\pi$), allowing the noise in the split outputs to fall below the standard quantum limit through proper positioning. A measurement-based feedback scheme can further suppress vacuum fluctuations at the other output, achieving sub-quantum-noise operation (e.g., at $z_2 = n \lambda/2$) by squeezing the input field and propagating it through the BS. The results offer a simple, boundary-condition–driven alternative to nonlinear squeezing techniques with broad applicability across frequencies and relevant to precision metrology and quantum information tasks.

Abstract

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.

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

TL;DR

By placing a mirror at the unused input port of a beam splitter, the authors engineer the spatial structure of vacuum modes and form a standing wave that modulates vacuum fluctuations at the outputs. Both semi-classical and quantum-operator analyses show that the standing-wave boundary condition creates nodes where vacuum noise vanishes (e.g., at ), allowing the noise in the split outputs to fall below the standard quantum limit through proper positioning. A measurement-based feedback scheme can further suppress vacuum fluctuations at the other output, achieving sub-quantum-noise operation (e.g., at ) by squeezing the input field and propagating it through the BS. The results offer a simple, boundary-condition–driven alternative to nonlinear squeezing techniques with broad applicability across frequencies and relevant to precision metrology and quantum information tasks.

Abstract

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.

Paper Structure

This paper contains 10 sections, 26 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Semi-classical Description of Fields and Noise
  3. Semiclassical Model of Coherent States
  4. Beam Splitter Configuration with Mirrors
  5. Conservation of Field Fluctuations
  6. Predicted Noise Characteristics of $E_1(z_1)$
  7. Quantum Mechanical Description of Fields
  8. Field Operators
  9. Measurement and Feedback Control of Vacuum Fluctuations
  10. Conclusion

Figures (2)

  • Figure 1: Schematic of the beam splitter (BS) setup. One input port of the beam splitter is the $b$ mode, and a mirror is placed at the other port. The modes $a_1$ and $a_2$ denote the two output ports of the BS.
  • Figure 2: Quantum noise characteristics divided by a beam splitter (BS). M denotes a mirror, and the two output ports of the BS are labeled as $a_1$ and $a_2$. At the mirror side, the noise forms a standing wave due to the boundary condition. The figure shows the case where $T = \frac{1}{2}$.