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arXiv:1412.7041 · Physical Review A

Nonlinear potential of a quantum oscillator induced by single photons

Ki-min Park B, Petr Marek, Radim Filip

Published Jul 3, 2014• 22 citations
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Abstract

Experimental investigation of the nonlinear dynamics of a quantum oscillator is a long-standing goal of quantum physics. We propose a conditional method for inducing an arbitrary nonlinear potential on a quantum oscillator weakly interacting with light. Such an arbitrary nonlinear potential can be implemented by sequential repetition of an elementary conditional $X$ gate. To implement the $X$ gate, a single photon is linearly coupled to the oscillator and is subsequently detected by optical homodyne detection.

DOI
10.1103/physreva.90.013804

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Experimental investigation of the nonlinear dynamics of a quantum oscillator is a long-standing goal of quantum physics. We propose a conditional method for inducing an arbitrary nonlinear potential on a quantum oscillator weakly interacting with light. Such an arbitrary nonlinear potential can be implemented by sequential repetition of an elementary conditional XXX gate. To implement the XXX gate, a single photon is linearly coupled to the oscillator and is subsequently detected by optical homodyne detection.
Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since strong highly nonlinear operations are often unavailable in the existing physical systems, it is a common practice to approximate them by using conditional measurement-induced methods. The conditional approach has several drawbacks, the most severe of which is the exponentially decreasing success rate of the strong and complex nonlinear operations. We show that by using a suitable two level system sequentially interacting with the oscillator, it is possible to resolve these issues and implement a nonlinear operation both nearly deterministically and nearly perfectly. We explicitly demonstrate the approach by constructing self-Kerr and cross-Kerr couplings in a realistic situation, which require a feasible dispersive coupling between the two-level system and the oscillator.
Quantum Optics With several techniques now available for generating single photons, coupled with their relative robustness and ability to be transmitted long distances, photons are ideal carriers of quantum information. However, determining the best methodol-ogy for detecting a single propagating photon without absorbing it (and destroying it) remains a work in progress. Xia et al. propose a cavity-free approach based on an induced nonlinear interaction. By co-propagating a weak probe beam with the signal beam containing the single photon in a nonlinear medium, they show theoretically that the phase of the probe beam should be shifted, conditional on the presence of the single photon. The proposed technique could offer a simpler route for implementing such quantum non-demolition detection strategies necessary for successful quantum information processing. Phys. Rev. Lett. 116 , 023601 (2016).
Photons are a promising candidate for quantum bits because their interaction with the environment is so weak that the quantum superposition state can easily be maintained. However, the construction of a quantum gate that controls one photon with another photon is a major challenge because of the difficulty of achieving photon-photon interaction. We show the realization of the quantum gates or devices which rely on quantum nonlinearity for photons induced with only linear optics. We also show that a quantum device using the induced nonlinearity is useful to verify quantum physics.
Photons are good candidates for carrying quantum information because they are very stable particles: they interact weakly with the medium and barely with each other. However, this has drawbacks when you want to process the information because, in this case, it is preferable to have photon-photon interactions. For example, for applications in quantum repeaters, such interactions would allow deterministic Bell state measurements, increasing the entanglement distribution rate between two remote nodes. Getting two photons to interact with each other efficiently requires mapping them into a nonlinear medium at the single-photon level, that is, a medium that reacts differently when it interacts with a single photon than when it does with two. Such strong nonlinearity has been demonstrated with Rydberg atoms, which are atoms excited to a state with a high principal quantum number. In this thesis we have performed nonlinear quantum optics experiments using an ensemble of cold Rydberg atoms, where we have studied the properties of the quantum light emitted by these atoms. First, we demonstrated nonlinearities at the single-photon level. To reach this stage, we made several improvements to the previous experimental setup available in the group, of which the implementation of a dipole trap was especially relevant. We evidence quantum nonlinearity by measuring photon antibunching for the transmitted light after interacting with the Rydberg state under electromagnetically induced transparency (EIT). We also showed the generation of single photons on-demand after storing weak coherent states of light pulses as collective Rydberg excitations. Then, we studied the variation of the light statistic throughout the output pulse after propagating through the medium as Rydberg polaritons, which are superposition states of light and Rydberg excitations. We showed that the properties at the beginning and the end of the pulse were different from those of the steady state. In particular, the light detected after the input pulse was abruptly turned off gave much stronger suppression of two-photon events. Then, we investigated how to exploit this effect to generate single photons on demand. To do this, we analyzed the quality of the single photons detected at the end of the pulse as a function of the detection probability and compared the results with those obtained by storing the input pulse as collective Rydberg excitations. We showed that the photons were generated more efficiently when increasing the detection window at the cost of deteriorating the single photons statistics. Finally, we investigated the indistinguishability of the photons emitted by our Rydberg atomic ensemble, a crucial property for using Rydberg atoms as nodes in quantum networks. We also compared the single photons generated after storage under EIT conditions with those obtained using a two-photon Raman excitation to the Rydberg state. We measured the indistinguishability by making them interfere with weak coherent states of light in a Hong-Ou-Mandel experiment. And we showed that, although we obtained better photon statistics under EIT conditions, the indistinguishability from those obtained with Raman excitation was significantly higher.
The realization of strong nonlinear interactions between individual light quanta (photons) is a long-standing goal in optical science and engineering, being of both fundamental and technological significance. We describe and demonstrate a medium that is nonlinear at the level of individual quanta, exhibiting strong absorption and phase shift for photon pairs while remaining transparent to single photons. The quantum nonlinearity is obtained by coherently coupling slowly propagating photons to strongly interacting atomic Rydberg states in a cold, dense atomic gas. Finally, we will discuss our progress towards realization of integrated quantum photonic systems, based on deterministic coupling of individual atoms and atom-like systems to photonic crystal cavities.
Detecting a single photon without absorbing it is a long-standing challenge in quantum optics. All experiments demonstrating the nondestructive detection of a photon make use of a high quality cavity. We present a cavity-free scheme for nondestructive single-photon detection. By pumping a nonlinear medium we implement an interfield Rabi oscillation which leads to a ∼π phase shift on a weak probe coherent laser field in the presence of a single signal photon without destroying the signal photon. Our cavity-free scheme operates with a fast intrinsic time scale in comparison with similar cavity-based schemes. We implement a full real-space multimode numerical analysis of the interacting photonic modes and confirm the validity of our nondestructive scheme in the multimode case.