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Physical Review A

Nonclassical two-photon interferometry and lithography with high-gain parametric amplifiers

Elna M. Nagasako, Sean J. Bentley, Robert W. Boyd, G. S. Agarwal

Published Sep 11, 2001• 52 citations
Publisher

Abstract

Optical parametric amplification is a process that leads to the generation of quantum states of light. In the limit of low single-pass gain, this process is often referred to as parametric down conversion, and produces entangled two-photon states. Such states have played a key role in recent studies of quantum optical effects such as quantum teleportation. As the gain of the parametric amplification process is increased, the generated light field still possesses strong quantum correlations, but not of the sort associated with two-photon states. Here we present an analysis of the output state of a parametric amplifier as a function of the single-pass gain, and we find certain signatures of quantum light (such as the vanishing of the coincidence rate in a Hong-Ou-Mandel interferometer) disappear in the high-gain limit, whereas others (such as the existence of two-photon interference fringes) remain. Consequently, the intense light field generated by a high-gain parametric amplifier can be utilized in such applications of quantum optics.

DOI
10.1103/physreva.64.043802

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Physical Review A•Apr 2, 2003•5 citations
Optical parametric amplification is a process that leads to the generation of quantum states of light. In the limit of low single-pass gain, this process is often referred to as parametric down conversion, and produces entangled two-photon states. Such states have played a key role in recent studies of quantum optical effects such as quantum teleportation. As the gain of the parametric amplification process is increased, the generated light field still possesses strong quantum correlations, but not of the sort associated with two-photon states. Here we present an analysis of the output state of a parametric amplifier as a function of the single-pass gain, and we find certain signatures of quantum light (such as the vanishing of the coincidence rate in a Hong-Ou-Mandel interferometer) disappear in the high-gain limit, whereas others (such as the existence of two-photon interference fringes) remain. Consequently, the intense light field generated by a high-gain parametric amplifier can be utilized in such applications of quantum optics.
We present a theoretical analysis of the properties of an unseeded optical parametic amplifier (OPA) used as the source of entangled photons for applications in quantum lithography. We first study the dependence of the excitation rate of a two-photon absorber on the intensity of the light leaving the OPA. We find that the rate depends linearly on intensity only for output beams so weak that they contain fewer than one photon per mode. We also study the use of an N-photon absorber for arbitrary N as the recording medium to be used with such a light source. We find that the contrast of the interference pattern and the sharpness of the fringe maxima tend to increase with increasing values of N, but that the density of fringes and thus the limiting resolution does not increase with N. We conclude that the output of an unseeded OPA exciting an N-photon absorber provides an attractive system in which to perform quantum lithography.
The study of optical parametric amplifiers (OPAs) has been successful in describing and creating nonclassical light for use in fields such as quantum metrology and quantum lithography [Agarwal et al., J. Opt. Soc. Am. B 24, 2 (2007)]. In this paper we present the theory of an OPA scheme utilizing an entangled state input. The scheme involves two identical OPAs seeded with the maximally path-entangled $\ensuremath{\mid}N00N⟩$ state $(\ensuremath{\mid}2,0⟩+\ensuremath{\mid}0,2⟩)∕\sqrt{2}$. The stimulated amplification results in output state probability amplitudes that have a dependence on the number of photons in each mode, which differs greatly from two-mode squeezed vacuum. A large family of entangled output states are found. Specific output states allow for the heralded creation of N=4N=4N=4 N00NN00NN00N states, which may be used for quantum lithography, to write sub-Rayleigh fringe patterns, and for quantum interferometry, to achieve Heisenberg-limited phase measurement sensitivity.
Quantum lithography proposes to adopt entangled quantum states in order to increase resolution in interferometry. In the present paper we experimentally demonstrate that the output of a high-gain optical parametric amplifier can be intense yet exhibits quantum features, namely, sub-Rayleigh fringes, as proposed by [Agarwal et al., Phys. Rev. Lett. 86, 1389 (2001)]. We investigate multiphoton states generated by a high-gain optical parametric amplifier operating with a quantum vacuum input for gain values up to 2.5. The visibility has then been increased by means of three-photon absorption. The present paper opens interesting perspectives for the implementation of such an advanced interferometrical setup.
Parametric down-conversion (PDC) is mostly known in the low-gain (spontaneous) regime, in which the correlated photon pairs are produced. Spontaneous PDC (SPDC) plays a very important role for quantum optics as a variety of quantum states is produced via SPDC. In the high-gain case PDC leads to generation of bright states having up to hundreds mW mean power. With such states almost any nonlinear optical interaction or light-matter interaction becomes more efficient. Even being macroscopically bright, the produced states maintain nonclassical properties as, for example, the fluctuations of electric field quadratures are squeezed below the shot-noise level. The high-gain PDC could be used not only in the same applications as SPDC, it also can provide new ones. Apart from that the high-gain PDC has many remarkable spectral and statistical properties, which are in the focus of this work. The description starts from the PDC generation in normal and anomalous group velocity dispersion ranges. The spectrum and mode content of high-gain PDC is considered as well as their change with the parametric gain are demonstrated. Then, there are the interference effects emerging from the PDC correlations presented, namely the macroscopic analogue of the Hong-Ou-Mandel interference. In addition, it is shown how spatial and temporal walk-off matching could be used for the generation of giant narrowband twin beams. Finally, the statistical properties of high-gain PDC are reviewed as well as their use for multiphoton effects is demonstrated. Photon-number fluctuations of PDC are studied via normalized correlation functions and probability distributions. These fluctuations enhance the generation efficiency for multiphoton effects by orders of magnitude and lead to tremendously fluctuating light described by heavy-tailed photon-number probability distributions.
The fields of quantum and nonlinear optics have given rise to a variety of nonclassical states of light that have been proven to surpass certain limitations set by classical physics. Namely, certain squeezed and entangled states have been shown to beat the shot-noise limit when making precision phase measurements in interferometry, as well as write lithographic patterns that are smaller than classically allowed by the Rayleigh diffraction limit. Additionally, single-photon sources and entangled photon pairs have given rise to provably secure quantum key distribution for cryptography. Producing these quantum states of light has proven a difficult task. Nonlinear crystals, when pumped by a laser, produce pairs of single photons via the process of spontaneous parametric down conversion (SPDC). This process is mediated by the second order nonlinear susceptibility of the material. When pumped in a high gain regime, these crystals give rise to optical parametric amplification, which is a viable source of squeezed light. The vast majority of research in this area has focused on crystals that are seeded by vacuum in their two modes. This dissertation concerns the field of quantum nonlinear optics. It is an investigation into the processes that occur when nonlinear materials interact with the electromagnetic field on the single photon level. I have focused on seeding nonlinear crystals with quantum states of light, including single photons and entangled states. This process results in various states directly applicable to interferometry, imaging, and cryptography. Another application investigated is an absolute radiance measurement via stimulated parametric down conversion resulting from non-vacuum seeding of a nonlinear crystal. Additionally, other nonlinear processes, including four-wave mixing, nonlinear magneto-optical effects and coherent population trapping in warm atomic vapor involving quantum states of light are investigated. The process of seeding third-order nonlinear interactions, such as in atomic vapors, gives rise to a variety of interesting, nonclassical phenomena such as entangled image transfer and nonlocal imaging. Strong analogies between SPDC and four-wave mixing are drawn. I also experimentally show an all optical pi-only phase shift of one light beam via another in warm Cesium vapor.
Two-photon interferometric quantum photon lithography for light of wavelength \ensuremath{\lambda} is capable of beating the Rayleigh diffraction limit of resolution \ensuremath{\lambda}/4 to the level of \ensuremath{\lambda}/8. The required twin single-photon states ∣1〉a∣1〉b,|1{〉}_{a}|1{〉}_{b},∣1〉a​∣1〉b​, which are converted into maximally entangled states by a 50:50 beam splitter, can be generated from a nondegenerate parametric amplifier initially in vacuum states and with a weak pump field. Increasing the pump strength can slightly increase the production rate of the desired state and it will also increase the production of the twin two-photon states ∣2〉a∣2〉b,|2{〉}_{a}|2{〉}_{b},∣2〉a​∣2〉b​, which leads to an unwanted background term. In this paper we show that, assuming a weak pair coherent state as input to the amplifier, quantum interference can be used to quench the production of the ∣2〉a∣2〉b|2{〉}_{a}|2{〉}_{b}∣2〉a​∣2〉b​ state and to enhance the production of the ∣1〉a∣1〉b|1{〉}_{a}|1{〉}_{b}∣1〉a​∣1〉b​ state by almost sixfold.