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Optica

Filtering multiphoton emission from state-of-the-art cavity quantum electrodynamics

Carlos Sánchez Muñoz, Fabrice P. Laussy, Elena del Valle, C. Tejedor, Alejandro González-Tudela

Published Jan 5, 2018• 72 citations
Publisher

Abstract

Engineering multiphoton states is an outstanding challenge with applications in multiple fields such as quantum metrology, quantum lithography, or even biological sensing. State-of-the-art methods to obtain them rely on post-selection, multi-level systems, or Rydberg atomic ensembles. Recently, it was shown that a strongly driven two-level system interacting with a detuned cavity mode can be engineered to continuously emit n-photon states. In the present work, we show that spectral filtering of its emission relaxes considerably the requirements on the system parameters even to the more accessible bad-cavity situation, opening up the possibility of implementing this protocol in a much wider landscape of different platforms. This improvement is based on a key observation: in the imperfect case where only a certain fraction of emission is composed of n-photon states, these have a well-defined energy separated from the rest of the signal, which allows one to reveal and purify multiphoton emission just by frequency filtering. We demonstrate these results by obtaining analytical expressions for the relevant figures of merit of multiphoton emission, such as the n-photon coupling rate between cavity and emitter, the fraction of light emitted as n-photon states, and n-photon emission rates. This allows us to make a systematic study of such figures of merit as a function of the system parameters and demonstrate the viability of the protocol in several relevant types of cavity quantum electrodynamics setups, where we take into account the impact of their respective experimental limitations

DOI
10.1364/optica.5.000014

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Engineering multiphoton states is an outstanding challenge with applications in multiple fields such as quantum metrology, quantum lithography, or even biological sensing. State-of-the-art methods to obtain them rely on post-selection, multi-level systems, or Rydberg atomic ensembles. Recently, it was shown that a strongly driven two-level system interacting with a detuned cavity mode can be engineered to continuously emit n-photon states. In the present work, we show that spectral filtering of its emission relaxes considerably the requirements on the system parameters even to the more accessible bad-cavity situation, opening up the possibility of implementing this protocol in a much wider landscape of different platforms. This improvement is based on a key observation: in the imperfect case where only a certain fraction of emission is composed of n-photon states, these have a well-defined energy separated from the rest of the signal, which allows one to reveal and purify multiphoton emission just by frequency filtering. We demonstrate these results by obtaining analytical expressions for the relevant figures of merit of multiphoton emission, such as the n-photon coupling rate between cavity and emitter, the fraction of light emitted as n-photon states, and n-photon emission rates. This allows us to make a systematic study of such figures of merit as a function of the system parameters and demonstrate the viability of the protocol in several relevant types of cavity quantum electrodynamics setups, where we take into account the impact of their respective experimental limitations
Engineering multiphoton states is an outstanding challenge with applications in multiple fields, such as quan- tum metrology, quantum lithography or even biological systems. State-of-the-art methods to obtain them rely on post-selection, multi-level systems or Rydberg atomic ensembles. Recently, it was shown that a strongly driven two-level system interacting with a detuned cavity mode can be engineered to continuously emit n-photon states. In the present work, we show that spectral filtering of its emission relaxes considerably the requirements on the system parameters even to the more accessible bad-cavity situation, opening up the possibility of implementing this protocol in a much wider landscape of different platforms. This improvement is based on a key observation: in the imperfect case where only a certain fraction of emission is composed of n-photon states, these have a well defined energy separated from the rest of the signal, which allows to reveal and purify multiphoton emission just by frequency filtering. We demonstrate these results by obtaining analytical expressions for relevant figures of merit of multiphoton emission, such as the n-photon coupling rate between cavity and emitter, the fraction of light emitted as n-photon states, and n-photon emission rates. This allows us to make a systematic study of such figures of merit as a function of the system parameters and demonstrate the viability of the protocol in several relevant types of cavity QED setups, where we take into account the impact of their respective experimental limitations.
Multi-photon lasing has been realized in systems with strong nonlinear interactions between emitters and cavity modes, where single-photon processes are suppressed. Coherence between the internal states of a quantum emitter, or among multiple emitters, plays a key role. Such continuous nonclassical sources of light can find applications in quantum computation, quantum sensing, quantum metrology, and quantum communication. This thesis explores the multi-photon lasing phenomena in various quantum dot-photonic crystal cavity quantum electrodynamic (QED) setups. Exciton-phonon interactions are inevitable in such systems and are incorporated using the polaron-transformed master equation. The Born-Markov approximation is employed to obtain the reduced density matrix rate equation. Using quantum laser theory, we derived the Scully-Lamb laser rate equations and evaluated the single- and multi-photon excess emission rates defined as the difference between emission and absorption rates into the cavity mode without mean-field approximations. We investigated cooperative two-photon lasing, correlated emission lasing, hyperradiant lasing, non-degenerate two-mode two-photon lasing, and continuous variable entanglement in open quantum systems with single or multiple semiconductor quantum dots (two-level, three-level, and four-level) driven coherently/incoherently and coupled to single/ bimodal cavities.
We describe the emission, detection and structure of multiphoton states of light. We include the effect of frequency filtering, which describes, at a fundamental level, physical detection of a quantum emitter. The case of the spontaneous emission of Fock states is treated fully and analytically. We stress this picture by contrasting it to the numerical simulation of two-photon bundles emitted from a two-level system in a cavity. We show that dynamical factors exist that allow for a more robust multiphoton emission than spontaneous emission. We also describe how this relates to thermal light.
Single-photon purity is one of the most important key metrics of many quantum states of light. For applications in photonic quantum technologies, e.g. quantum communication and linear optical quantum computing, a minimization of the multi-photon error rate is required because of its error-introducing nature. Ultimately, the purity of state-of-the-art single-photon sources was found to be limited by spontaneous emission and subsequent reexcitation during the interaction with the driving field. Here, we demonstrate that even this fundamental limit to the single-photon purity can be overcome due to the distinct spectro-temporal properties of the individual photons forming multi-photon errors. For driving pulses shorter than the emitter lifetime, we find that photons emitted during the pulse exhibit a significantly broader spectral shape than the emitter's natural linewidth. Thus, we can selectively filter out the majority of this instantaneously emitted photon by employing narrowband spectral filters, which reduces the measured degree of second-order coherence at zero time delay by almost one order of magnitude. This enables a significant suppression of the multi-photon error rate without detrimental effects on the desired single-photon emission.
Abstract Engineering multiphoton resources is of importance in quantum metrology, quantum lithography, and biological sensing. Here we propose a concept of dynamical emission of N strongly-correlated photons. This is realized in a circuit quantum electrodynamical system driven by two Gaussian-pulse sequences. The underlying physical mechanism relies on the stimulated Raman adiabatic passage that allows efficient and selective preparation of target multiphoton states. Assisted by the photon decay, a highly pure N-photon bundle emission takes place in this system. In particular, the dynamical N-photon bundle emission can be tuned by controlling the time interval between consecutive pulses so that the device behaves as an N-photon gun, which can be triggered on demand. Our work opens up a route to achieve multiphoton source devices, which have wide potential applications in quantum information processing and quantum metrology.
The purpose of this paper is to derive filters for an arbitrary open quantum system driven by a light wave packet prepared in a continuous-mode multiphoton state. A continuous-mode multiphoton state is a state of a traveling light wave packet that contains a definite number of photons and is characterized by a temporal (or, equivalently, spectral) profile. After the interaction with the system, the outgoing light can be monitored by means of homodyne detection or photodetection. Filters for both measurement schemes are derived in this paper. Unlike the vacuum or the coherent state case, the annihilation operator of the light field acting on a multiphoton state changes the state by annihilating a photon, and this makes the traditional filtering techniques inapplicable. To circumvent this difficulty, we adopt a non-Markovian embedding technique proposed in [J. E. Gough, M. R. James, and H. I. Nurdin, Quantum Inf. Process., 12 (2013), pp. 1469--1499] for the study of the single-photon filtering problem. However, the multiphoton nature of the problem addressed in this paper makes the study much more mathematically involved. Moreover, as demonstrated by an example---a two-level system driven by a continuous-mode two-photon state---multiphoton filters can reveal interesting strong nonlinear optical phenomena absent in both the single-photon state case and the continuous-mode Fock state case.