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arXiv:quant-ph/0401088 · Physical Review Letters

Two Photon Absorption and Coherent Control with Broadband Down-Converted Light

Barak Dayan, Avi Pe’er, Asher A. Friesem, Yaron R. Silberberg

Published Jul 9, 2004• 252 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate two-photon absorption with broadband down-converted light (squeezed vacuum). Although incoherent and exhibiting the statistics of a thermal noise, broadband down-converted light can induce two-photon absorption with the same sharp temporal behavior as femtosecond pulses, while exhibiting the high spectral resolution of the narrow band pump laser. Using pulse-shaping methods, we coherently control two-photon absorption in rubidium, demonstrating spectral and temporal resolutions that are 3-5 orders of magnitude below the actual bandwidth and temporal duration of the light itself. Such properties can be exploited in various applications such as spread-spectrum optical communications, tomography, and nonlinear microscopy.

DOI
10.1103/physrevlett.93.023005

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We experimentally demonstrate two-photon absorption with broadband down-converted light (squeezed vacuum). Although incoherent and exhibiting the statistics of a thermal noise, broadband down-converted light can induce two-photon absorption with the same sharp temporal behavior as femtosecond pulses, while exhibiting the high spectral resolution of the narrow band pump laser. Using pulse-shaping methods, we coherently control two-photon absorption in rubidium, demonstrating spectral and temporal resolutions that are 3-5 orders of magnitude below the actual bandwidth and temporal duration of the light itself. Such properties can be exploited in various applications such as spread-spectrum optical communications, tomography, and nonlinear microscopy.
We report the experimental demonstration of coherent control with high power, broadband squeezed vacuum. Although incoherent and exhibiting the statistics of a thermal noise, broadband squeezed vacuum is shown to induce certain two-photon interactions as a coherent ultrashort pulse with the same spectral bandwidth. Utilizing pulse-shaping techniques we coherently control the sum-frequency generation of broadband squeezed vacuum over a range of two orders of magnitude. Coherent control of two-photon interactions with broadband squeezed vacuum can potentially obtain spectral resolutions and extinction ratios that are practically unattainable with coherent pulses.
The coherence properties of broadband down converted light are investigated theoretically and experimentally in both the classical and quantum mechanical frameworks. Although broadband down converted light is one-photon incoherent noise, it possesses unique two-photon coherence. Thus, for performing two-photon processes, down-converted light is equivalent to coherent ultrashort pulses in some aspects and to coherent CW laser radiation in others. This equivalence is theoretically established and experimentally demonstrated in the classical, high-power regime. Two applications that take advantage of multi-photon coherence are then described in detail; one for optical spread spectrum communication and the other for sub-diffraction limit optical lithography. A key part of this research is the design and implementation of an efficient source that generates high-power broadband down conversion in a cavity. A broadband oscillation in the cavity is ensured by a mechanism very similar to passive mode-locking of ultrashort pulse laser sources, which we term as pair-wise mode locking, thus extending the equivalence to ultrashort pulses to the light generating sources also. Finally, the quantum mechanical properties of broadband down-conversion are explored experimentally, by performing a two-photon process (sum frequency generation) at the low power level of entangled photon pairs. The non-classical nature of the light is expressed by a linear intensity dependence of the non-linear process. Temporal shaping with femtosecond resolution of the entangled photon pairs is demonstrated using this non-linear interaction.
i1 Abstract: We report twocontrol experiments that exploit thecoherent correlations within the spectrum ofincoherent broadband down-converted light todemonstrate ultrahigh spectral and temporal resolutions athigh power andinherent non-classical features atlowpower. c2005Optical Society ofAmerica OCIScodes: (270.6570)Squeezed states, (270.4180)Multiphoton processes, (320.5540) Pulse shaping. Eventhough broadband down-converted light that isgenerated byanarrowband pumpcanbeconsidered as incoherent white noise, itpossesses phase andamplitude correlations between thecorresponding signal-idler modes ES(co) = E,(co, -to). Asaresult, thesignal andtheidler fields arecomplex conjugated white noise fields (1). The signal-idler correlations areinherently non-classical since their precision exceeds theclassical limit (sub-shot noise). Inthefollowing wedescribe twocoherent control experiments that exploit this coherent phase relation: One experiment demonstrates control overtwo-photon absorption (TPA) with high-power broadband down-conversion, where thetemporal resolution ofultrashort pulses iscombined with anultrahigh spectral resolution that isotherwise unattainable (1). Another experiment demonstrates control oversum-frequency generation (SFG) intheinherently non-classical low-power regime ofentangled photons. Inthat regime SFGserves asanultrafast coincidence detector andspectral phase manipulations directly affect thetwo-photon wavefunction (2,3). 1.Coherent control oftwo-photon absorption athigh-power. Theexcitation ofanarrow twophoton transition (atfrequency coo) withbroadband light isinsensitive toananti- symmetric spectral phase around tco02 (4). Since thespectral phase ofdown-converted light isanti-symmetric around thepumpfrequency c/pl2, theexcitation isasefficient aswithatransform-limited
When two-photon interactions are induced by down-converted light with a bandwidth that exceeds the pump bandwidth, they can obtain a behavior that is pulselike temporally, yet spectrally narrow. At low photon fluxes this behavior reflects the time and energy entanglement between the down-converted photons. However, two-photon interactions such as two-photon absorption (TPA) and sum-frequency generation (SFG) can exhibit such a behavior even at high power levels, as long as the final state (i.e., the atomic level in TPA, or the generated light in SFG) is narrow-band enough. This behavior does not depend on the squeezing properties of the light, is insensitive to linear losses, and has potential applications. In this paper we describe analytically this behavior for traveling-wave down conversion with continuous or pulsed pumping, both for high- and low-power regimes. For this we derive a quantum-mechanical expression for the down-converted amplitude generated by an arbitrary pump, and formulate operators that represent various two-photon interactions induced by broadband light. This model is in excellent agreement with experimental results of TPA and SFG with high-power down-converted light and with entangled photons [Dayan et al., Phys. Rev. Lett. 93, 023005 (2004); 94, 043602 (2005); Pe'er et al., ibid. 94, 073601 (2005)].
We present an analytical quantum theoretic model for nonresonant molecular two-photon absorption (TPA) of broadband, spectrally multimode squeezed vacuum, including low-gain (isolated entangled photon pairs) and high-gain (bright squeezed vacuum or BSV) regimes. The results are relevant to the potential use of entangled-light TPA as a spectroscopic and imaging method. We treat the scenario that the exciting light is spatially single mode and is nonresonant with all intermediate molecular states. In the case of high gain, we find that in the case that the linewidth of the final molecular state is much narrower than the bandwidth of the exciting light, bright squeezed vacuum is found to be equally (but no more) effective in driving TPA as is a quasimonochromatic coherent-state (classical) pulse of the same temporal shape, duration, and mean photon number. Therefore, in this case the sought-for advantage of observing TPA at extremely low optical flux is not provided by broadband bright squeezed vacuum. In the opposite case that the final-state linewidth is much broader than the bandwidth of the BSV exciting light, we show that the TPA rate is proportional to the second-order intensity autocorrelation function at zero time delay g(2)(0){g}^{(2)}(0)g(2)(0), as expected. We derive and evaluate formulas describing the transition between these two limiting cases, that is, including the regime where the molecular linewidth and optical bandwidth are comparable, as is often the case in experimental studies. We also show that for g(2)(0){g}^{(2)}(0)g(2)(0) to reach the idealized form g(2)(0)=3+1/n‾{g}^{(2)}(0)=3+1/\overline{n}g(2)(0)=3+1/n, with n‾\overline{n}n being the mean number of photons per temporal mode, it is required to compensate the dispersion inherent in the nonlinear-optical crystal used to generate the BSV.