In this blog post, I explore the measurement of a quantum state's quadrature using a balanced beam splitter and a quasi-classical state. By analyzing the expectation value and variance of the difference in photon numbers at the output ports, I show how, in the specific case of a balanced Mach-Zehnder interferometer with a strong quasi-classical state in one input channel, the measurement effectively extracts the P quadrature of the quantum state in the other input channel. This method provides a way to characterize the statistical properties of the input quantum state, including vacuum fluctuations, through repeated measurements of the balanced signal.
In this blog post, I examine the quantum nature of noise in Mach-Zehnder interferometers. My analysis shows that even with intense laser beams, noise is fundamentally limited by quantum mechanics, specifically by vacuum fluctuations entering the interferometer's unused port. This perspective contrasts with classical interpretations of noise as mere detector imperfections. Understanding noise as a consequence of vacuum fluctuations opens avenues for quantum noise reduction techniques.
In this blog post, I explore the measurement using interferometers. Although gravitational wave detectors employ more complex interferometers, I will use the Mach-Zehnder interferometer as a straightforward illustration of the sensitivity improvement principle. I derive the output operators for this interferometer and calculate the expected photon counts at its output ports. This analysis reveals the sinusoidal dependence of photon counts on the phase difference between the interferometer arms, demonstrating how phase adjustments influence the output.
In this blog post, I explore the fragility of squeezed states, a quantum resource vital in precision measurements. Squeezing, while powerful, is highly susceptible to optical losses such as absorption or imperfect detection. I use a beam splitter model to represent these losses and mathematically analyze how they introduce vacuum noise, ultimately diminishing the benefits of squeezing. This analysis reveals why maintaining low-loss conditions is critical for successful implementation of squeezed states, especially in demanding applications like gravitational wave detection.
このブログ投稿では、位相スクイーズド状態を示す私の最新の量子光学シミュレーションを共有します。この量子ノイズの操作は、重力波検出や超精密測定に実用的な応用があります。このビジュアライゼーションでは、量子不確定性が位相空間でどのように進化し回転するかを見ることができ、この魅力的な量子現象の明確な描像を提供します。
In questo post del blog, condividerò la mia ultima simulazione di ottica quantistica che mostra gli stati compressi di fase. Questa manipolazione del rumore quantistico ha applicazioni pratiche nel rilevamento delle onde gravitazionali e nelle misurazioni ultra-precise. In questa visualizzazione, si può vedere come l'incertezza quantistica evolve e ruota nello spazio delle fasi, offrendo un'immagine chiara di questo affascinante fenomeno quantistico.
In this blog post, I will to share my latest quantum optics simulation showcasing phase-squeezed states. This manipulation of quantum noise has practical applications in gravitational wave detection and ultra-precise measurements. In this visualization, you can see how the quantum uncertainty evolves and rotates in phase space, giving a clear picture of this fascinating quantum phenomenon.
In this blog post, I present a series of simulations visualizing fundamental concepts in quantum optics. These videos explore the quantum-coherent evolution of the electric field and delve into the dynamics of squeezed states, both with positive and negative squeezing. By observing these simulations, you can gain a visual understanding of how quantum uncertainty behaves during phase evolution and how squeezing manipulates quantum fluctuations.
In this blog post, I explore the representation squeezed states of light in the phasor plane and their application in enhancing measurement precision. I will show how, unlike classical light sources, squeezed light allows for more accurate measurements, particularly of amplitude and phase, without the need for increased beam power. This is especially beneficial for delicate samples that are sensitive to high intensity light. I will discuss the underlying physics and the practical advantages of using squeezed light to push the boundaries of measurement accuracy beyond the standard quantum limit.
In this blog post, I explore the fascinating realm of squeezed states of light and how they allow us to achieve measurement precision beyond the standard quantum limit. Before their discovery, the shot noise was believed to be an unbreakable barrier in optical measurements. However, squeezed states, with their reduced fluctuations in specific observables, offer a pathway to surpass this limit. Focusing on quadrature components and balanced homodyne detection, I will show how these states enable amplitude or phase measurements with unprecedented accuracy, opening new possibilities in fields like gravitational wave detection and quantum metrology.
In this blog post, I continue my investigation into squeezed states of light, specifically examining the case where the squeezing parameter R is positive. I illustrate how, in the positive case, the dispersion of the electric field is minimized at different times compared to the negative case, while still exhibiting an elliptical shape in the complex plane. By visualizing this rotating ellipse, I show how the squeezed state achieves reduced fluctuations in a specific quadrature, maintaining the Heisenberg uncertainty principle, and contrasting it with the constant dispersion of quasi-classical states.
In this blog post, I explore squeezed states of light and their representation in the complex plane. I show how, unlike classical states with their uniform dispersion, squeezed states exhibit an elliptical dispersion that rotates with the complex amplitude. By visualizing the electric field average and dispersion, I clarify how squeezed states achieve reduced variance in one quadrature at the expense of increased variance in the other, always respecting the Heisenberg uncertainty principle. This visual approach offers a clear understanding of these quantum states.
In this blog post, I present the detailed calculation of the average electric field and its variance for squeezed quantum states. I show step-by-step how these fundamental quantities are derived for a squeezed state, contrasting them with the behavior observed in quasi-classical states. My analysis reveals a key characteristic of squeezed states, their electric field variance is not constant. Instead, it exhibits a dependence on both position and time, unlike the constant variance in quasi-classical scenarios. This space-time variation underscores a significant distinction in the statistical nature of the electric field when comparing squeezed and coherent states, offering a deeper appreciation for the quantum properties of squeezed light.
In this blog post, I introduce squeezed states of light, a concept from quantum optics developed in the 1980s. These states are eigenstates of a generalized annihilation operator, offering capabilities beyond the standard quantum limit for measurement precision. I will present the definition of these squeezed states, comparing them to quasi-classical states. I will also discuss their properties using generalized annihilation and creation operators. This post provides an overview of these interesting quantum states and their potential.
In this blog post, I explore the time evolution of the electric field average and its dispersion for quasi-classical states. I visualize this evolution using a rotating complex amplitude and a disk representing the dispersion. This approach allows for a clear understanding of the field's dynamics, contrasting with the static quadrature representation measurable in experiments. I highlight the difference between these two perspectives, emphasizing the time-dependent nature of the field evolution and the time-independent nature of quadrature measurements, offering a visual tool for understanding quantum states.