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Generation of Squeezed States by Parametric Down Conversion
Abstract
Squeezed states of the electromagnetic field are generated by degenerate parametric down conversion in an optical cavity. Noise reductions greater than 50% relative to the vacuum noise level are observed in a balanced homodyne detector. A quantitative comparison with theory suggests that the observed squeezing results from a field that in the absence of linear attenuation would be squeezed by greater then tenfold.
... A prominent example of non-classical states is the set of squeezed states, in which the fluctuation associated with one quadrature component is below the vacuum state 39 . Early theoretical work in the 60s and 80s led to the conclusion that quantum fluctuations can be reduced below the shot noise in many forms of nonlinear optical interactions [40][41][42] . For example, squeezed states are produced in nonlinear processes called degenerate parametric down-conversion, where a "classical" electromagnetic field drives a nonlinear www.nature.com/scientificreports/ ...
At the heart of quantum thermodynamics lies a fundamental question about what is genuine “quantum” in quantum heat engines and how to seek this quantumness, so that thermodynamical tasks could be performed more efficiently compared with classical protocols. Here, using the concept of P-representability, we define a function called classicality, which quantifies the degree of non-classicality of bosonic modes. This function allows us to explore the role of non-classicality in quantum heat engines and design optimal protocols for work extraction. For two specific cycles, a quantum Otto and a generalised one, we show that non-classicality is a fundamental resource for performing thermodynamic tasks more efficiently.
... The generation of squeezed states usually requires a nonlinear optical process due to its nonlinear photon statistics. Squeezed light was first produced using atomic sodium as a nonlinear medium via four-wave mixing in 1985 [13] and was soon followed with experiments employing optical fibers [14], nonlinear crystals [15] and semiconductor laser [16]. After that, a variety of schemes and more substantial squeezing (up to 15 dB [17]) have been predicted theoretically and realized experimentally with the rapidly development of quantum technology. ...
We propose that the squeezed light accompanied by hyperradiance is induced by quantum interference in a linear system consisting of a high quality optical cavity and two coherently driven two-level qubits. When two qubits are placed at the crest and trough of the standing wave in the cavity respectively (i.e., they have the opposite coupling coefficient to the cavity), we show that squeezed light is generated in the hyperradiance regime under the conditions of strong coupling and weak driving. Simultaneously, the Klyshko's criterion alternates up and down at unity when the photon number is even or odd. Moreover, the orthogonal angles of the squeezed light can be controlled by adjusting the frequency detuning pressure between the driving field and the qubits. It can be implemented in a variety of quantum systems, including but not limited to two-level systems such as atoms, quantum dots in single-mode cavities.
... The abrupt discontinuity at the first-order transition point and the associated spectral bi-stability can open new possibilities in the domain of precision sensing (see Supplementary section 6). The semi-classical regime considered in this work can be probed below the oscillation threshold [52], where a quantum image of the above threshold spectral phase transition exists, which may lead to the co-existence of a quantum phase transition (see Supplementary section 7) [53]. Our study mainly focuses on the adiabatic regime where the control parameter is varied gradually. ...
Phase transitions and the associated symmetry breaking are at the heart of many physical phenomena. Coupled systems with multiple interacting degrees of freedom provide a fertile ground for emergent dynamics that is otherwise inaccessible in their solitary counterparts. Here we show that coupled nonlinear optical resonators can undergo self-organization in their spectrum leading to a first-order phase transition. We experimentally demonstrate such a spectral phase transition in time-multiplexed coupled optical parametric oscillators. We switch the nature of mutual coupling from dispersive to dissipative and access distinct spectral regimes of the parametric oscillator dimer. We observe abrupt spectral discontinuity at the first-order transition point which can pave the way for the realization of novel transition-edge sensors. Furthermore, we show how non-equilibrium phase transitions can lead to enhanced sensing, where the applied perturbation is not resolvable by the underlying linear system. Our results can pave the way for sensing using nonlinear driven-dissipative systems leading to performance enhancements without sacrificing sensitivity.
... where ξ = re iθ with real r (squeezing parameter) and 0 θ 2π. Experimental realization of this state was achieved way back in 1985-1986 [30,31]. In the recent years, great progress in the generation of this state have been achieved [18,[32][33][34] that could significantly improve quantum information applications. ...
We have classified the superposition of squeezed wavepackets into two kinds and studied their quadrature squeezing. We have shown that the squeezing and higher-order squeezing in the quadrature disappear for the states of the first kind. However, for the second kind, it is possible to achieve the maximum amount of squeezing by adjusting the parameters in the superposition. The absence of squeezing for the superposition states is explained based on the expectation value of the energy density. We find that the expectation value of energy density in quantum wavepackets that shows no squeezing is positive. The energy density in the decoherence dynamics of single and two-mode squeezed states is also carried out. Our further analysis shows that different types of squeezed states, including states which are not wavepackets, exhibit negative energy density.
量子測定における重要な基礎理論のひとつに量子仮説検定・推定理論がある。量子通信であれば元の量子信号が何だったかを判別する必要があるし、量子計算などの量子過程後なら出力された量子信号はやはり、どの信号だったかを判別する必要があるからである。
受信した信号が既知の集合のどれかという仮説を立て、「尤もらしい」ものを選択することを仮説検定と呼ぶ。さらに量子推定理論は受信した量子信号が持つパラメータを尤もらしい中から最尤推定する理論である。
量子測定の結果は確率的なものである。しかし古典の場合でも、通信または古典過程後において、雑音による確率的な測定誤差が起こりうる。つまり確率過程を通じ、古典仮説検定・推定理論は自然に量子仮説検定・推定理論に拡張できる。本稿を通し測定の量子/古典対応の理解を深めて頂ければ幸甚である。
本理論は上述の通り量子測定に関する重要な知見を提供する。それにも関わらず英書でも和書であっても近年の著書が少ない。英書ならば、C. W. ヘルストロームの 1976 年の著書[1]以降[2, 3]が出版されたが、本稿で著者が伝えたい範囲を全て記載しているわけではないし初学者には敷居が高すぎる。和書[4]も絶版になってしまった。現存する和書では、文献[5]が量子仮説検定を扱うが、これも著者が伝えたい範囲を全て記載しているわけではない。また、著者の知る限り文献[1]も2012年ごろに復刊したがやはり絶版の危機にはあった。
もちろん著者より本論に秀でた専門家は少ないながらも国内外に存在するため、彼らが執筆した優れた文献を見つけることもできる。しかし理論の存在すら知られてなければ、当該文献が検索されることもない。近年の著者の研究活動を通じて本分野の重要さを痛感しながらも、量子情報の研究に携わる多くの研究者にあまり知られずにいる状況を鑑み、僭越ながら本稿の執筆者が記述させて頂くことにした。しかし前述したように既知の書籍でも基礎的なことは十分に網羅されている。そこで、本稿では本分野の最近の発展も紹介したいと思う。本稿の執筆者の理解に足りないところがあればご指摘をいただけると幸いであるし、より良い教科書を執筆していただければなお幸いである。
本稿の構成は以下の通りである。まず2節では仮説検定や量子状態についての基本的用語を概説する。3節では、前述した2元量子ベイズ検定理論を例として概説し、本節以降を理解するための基本的知識を提供する。さらに、古典状態検定理論と量子状態検定理論の類似点と相違点についても概説する。通常ならば量子拡張される前の古典状態検定理論を先に説明することが多いが、違いを際立たせるため量子論を先に記述する。4節では前節の検定を多元量子ベイズ識別へと拡張する。さらに数学的に整理された例としてユニタリ変換対称性のある有限/無限次元ヒルベルト空間上の量子状態への適用について記述する。5節では、量子センサーに重要な概念である量子ネイマン・ピアソン検定を解説する。量子検定理論は6節の量子ミニマックス検定で締めくくられる。本検定は、量子ベイズ検定では解き難い問題に対して準最適解を与えるが主眼はそこではなく、送信者が受信者の測定誤りを最大にするよう仕掛けながら受信者は最大の成功確率を達成する2者間ゲームの記述である。これは自然現象との対話モデルとも言える。つまり何が尤もらしいかは観測者にはわからず、尤もらしい自然現象を記述する理論を、観測結果により採択する科学的過程のひとつである。
量子検定理論の説明がひととおり終わった後は、7節で量子推定理論の解説を行う。本論は、有限個の量子状態のうち正しい量子状態を高確率で検出できるかという量子検定理論とは異なり、連続量である量子状態の持つパラメータを、最尤推定するための手法である。やや粗い説明をすれば、量子仮説検定理論において既知な量子状態の数を、無限大へと増やしたものである。またパラメータ推定誤差について量子クラメール・ラオ不等式を用いて解説する。その理由は統計量を平均値のみで議論することは退けるべきであり、必ず推定の確からしさ(分散または誤差など)を論ずるべきだからである。最後に8節では、非可換量同時測定についての既知の理論を概説する。非可換量同時測定とは、量子力学における不確定性関係における相補的な物理量の同時測定を意味する。
以上の7節を通し9節では、3節から8節までの近年の発展を紹介し、最後に10節で参考文献を列記する。しかしただ列記しただけでは、どの文献が各読者にとって重要かを判別しかねると考え、各文献についての説明をいくらか加えることにする。
[in English by DeepL] One of the important basic theories in quantum measurement is the quantum hypothesis testing and estimation theory. This is because it is necessary to determine what the original quantum signal was in the case of quantum communication, and it is also necessary to determine what the output quantum signal was after a quantum process such as quantum computation.
The hypothesis that the received signal is one of a set of known signals and selecting the "plausible" one is called hypothesis testing. Furthermore, quantum estimation theory is the theory of maximum likelihood estimation of the parameters of the received quantum signal from among the plausible ones.
The results of quantum measurements are probabilistic. However, even in the classical case, stochastic measurement errors due to noise can occur in the communication or after the classical process. Thus, through stochastic processes, classical hypothesis testing and estimation theory can be naturally extended to quantum hypothesis testing and estimation theory. We hope that this paper will deepen your understanding of the quantum/classical correspondence in measurement.
As mentioned above, this theory provides important insights into quantum measurement. Nevertheless, there have been few recent publications of this theory, either in English or Japanese. For English books, C. W. Hellstrom's 1976 book [1] and subsequent books [2, 3] have been published, but they do not cover the entire scope of what the author wishes to convey in this paper, and are too difficult for beginning students to read. The Japanese book [4] is also out of print. Among the existing Japanese books, Reference [5] deals with quantum hypothesis testing, but it too does not cover all the topics the author wishes to convey. As far as the author knows, Reference [1] was also reprinted around 2012, but was still in danger of going out of print.
Of course, there are a small number of experts in Japan and abroad who are better at this theory than the author, and it is possible to find excellent references written by them. However, if the theory is not even known to exist, the relevant literature will not be searched. Although the author is keenly aware of the importance of this field through his research activities in recent years, it is not well known to many researchers involved in the study of quantum information, and therefore, the author of this paper has decided to write about it. However, as mentioned above, the fundamentals of the field are well covered in known books. Therefore, in this paper, we would like to introduce some recent developments in this field. We would be grateful if you could point out any gaps in the understanding of the authors of this paper, and we would be even more grateful if you could write a better textbook.
The structure of this paper is as follows. Section 2 outlines the basic terminology of hypothesis testing and quantum states, and Section 3 outlines the aforementioned two-way quantum Bayesian test theory as an example to provide the basic knowledge for understanding the rest of this paper. It also outlines the similarities and differences between classical and quantum state test theories. Section 4 extends the tests of the previous section to multi-quantum Bayesian identification. Section 5 describes the quantum Neyman-Pearson test, an important concept for quantum sensors. Quantum test theory concludes with the quantum minimax test in section 6. This test provides a quasi-optimal solution to a problem that is difficult to solve with the quantum Bayesian test, but its main focus is not on that, but on the description of a two-party game in which the sender tricks the receiver into maximizing the receiver's measurement error while the receiver achieves maximum probability of success. This can be described as a model of interacting with natural phenomena. In other words, it is a scientific process in which the observer does not know what is plausible, but adopts a theory that describes a plausible natural phenomenon based on the results of observation.
After a brief explanation of quantum test theory, we will discuss quantum estimation theory in section 7. Unlike quantum test theory, which is concerned with the probability of detecting the correct quantum state among a finite number of quantum states, this theory is a method for maximum likelihood estimation of the parameters of a quantum state, which is a continuous quantity. In a rather crude explanation, it is a method to increase the number of known quantum states in quantum hypothesis testing theory to infinity. The parameter estimation error is also explained using the quantum Clamor-Rao inequality. The reason for this is that one should avoid discussing statistics only in terms of mean values, and should always discuss the certainty of the estimation (variance, error, etc.). Finally, Section 8 outlines the known theory of simultaneous measurement of noncommutative quantities. Noncommutative coincidence refers to the simultaneous measurement of complementary physical quantities in the uncertainty relation in quantum mechanics.
Section 9, through the above seven sections, introduces the recent developments from Section 3 to Section 8, and finally Section 10 lists the references. However, we believe that a mere list of references is not enough to identify which ones are important for each reader, so we will add some explanations for each reference.
In this project, we study the time dynamics of quantum gates proposed in J. Phys. B: At. Mol. Opt. Phys 52, 205502 (2019) in a system of coupled harmonic oscillators. In particular, we focus on the realization of two-qubit gates such as the CNOT gate and quantum phase gate. These gates operate on qubits which could be prepared by truncating the infinite-dimensional energy levels of the harmonic oscillators.
We show that all the minimum uncertainty packets are unitarily equivalent to the coherent states and that coherence is in fact stationary minimality.
In a previous paper we have shown that all minimum-uncertainty packets are unitarily equivalent to the coherent states and that coherence may be viewed as stationary minimality. In this note we give some additional information relating to the nature of the unitary-equivalence structure. We also give a new calculation of some matrix elements of the operator that implements the unitary equivalence which is not subject to the shortcoming inherent in the original calculation.
We describe a new and highly effective optical frequency discriminator and laser stabilization system based on signals reflected from a stable Fabry-Perot reference interferometer. High sensitivity for detection of resonance information is achieved by optical heterodyne detection with sidebands produced by rf phase modulation. Physical, optical, and electronic aspects of this discriminator/laser frequency stabilization system are considered in detail. We show that a high-speed domain exists in which the system responds to the phase (rather than frequency) change of the laser; thus with suitable design the servo loop bandwidth is not limited by the cavity response time. We report diagnostic experiments in which a dye laser and gas laser were independently locked to one stable cavity. Because of the precautions employed, the observed sub-100 Hz beat line width shows that the lasers were this stable. Applications of this system of laser stabilization include precision laser spectroscopy and interferometric gravity-wave detectors.
Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctuations, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50-50 beam splitter. This result also demonstrates the fact that the basic quantum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise.
A general approach, within the framework of canonical quantization, is described for analyzing the quantum behavior of complicated electronic circuits. This approach is capable of dealing with electrical networks having nonlinear or dissipative elements. The techniques are applied to circuits capable of generating squeezed-state or two-photon coherent-state signals. Circuits capable of performing back-action-evading electrical measurements are also discussed.
The problem of detecting a coherent light beam in the presence of unwanted background radiation by the heterodyne method is examined. For a sufficiently strong local-oscillator field, the detectability of the signal is unaffected by the presence of the background radiation. It is shown that, in general, there exists an optimum receiver size that maximizes the signal-to-noise ratio. This result is illustrated by several examples. A procedure for the detection of a light signal of unknown direction is suggested.
The properties of a unique set of quantum states of the electromagnetic field are reviewed. These 'squeezed states' have less uncertainty in one quadrature than a coherent state. Proposed schemes for the generation and detection of squeezed states as well as potential applications are discussed.
It is pointed out that single-frequency emission from a Nd:YAG laser at
1.06 microns at power levels in excess of 1 W would be useful for the
investigation of dynamic processes in nonlinear optics. The emission
could also be important for applications related to high-resolution
nonlinear spectroscopy. However, due to thermal loading of the laser
rod, it is very difficult to obtain submegahertz frequency stability for
Nd:YAG lasers at high levels of lamp pumping power. The present
investigation is concerned with a single-frequency Nd:YAG laser with an
output power exceeding 1.1 W and a frequency stability of 120-kHz rms.
This performance is obtained in a ring cavity. This approach makes it
possible to eliminate problems associated with spatial hole burning. The
ring cavity is designed to minimize laser fluctuations due to noise in
the pumping and cooling processes.
Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctuations, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50-50 beam splitter. This result also demonstrates the fact that the basic quantum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise.
The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.