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arXiv:2103.12041 · Science Advances

Unconditional Fock state generation using arbitrarily weak photonic nonlinearities

Andrew Lingenfelter, David C K Roberts, Aashish A. Clerk

Published Nov 26, 2021• 28 citations
arXivHTMLPDF

Abstract

We present a mechanism that harnesses extremely weak Kerr-type nonlinearities in a single driven cavity to deterministically generate single-photon Fock states and more general photon-blockaded states. Our method is effective even for nonlinearities that are orders-of-magnitude smaller than photonic loss. It is also completely distinct from so-called unconventional photon blockade mechanisms, as the generated states are non-Gaussian, exhibit a sharp cutoff in their photon number distribution, and can be arbitrarily close to a single-photon Fock state. Our ideas require only standard linear and parametric drives and are hence compatible with a variety of different photonic platforms.

DOI
10.1126/sciadv.abj1916

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We present a mechanism that harnesses extremely weak Kerr-type nonlinearities in a single driven cavity to deterministically generate single-photon Fock states and more general photon-blockaded states. Our method is effective even for nonlinearities that are orders-of-magnitude smaller than photonic loss. It is also completely distinct from so-called unconventional photon blockade mechanisms, as the generated states are non-Gaussian, exhibit a sharp cutoff in their photon number distribution, and can be arbitrarily close to a single-photon Fock state. Our ideas require only standard linear and parametric drives and are hence compatible with a variety of different photonic platforms.
The development of many scalable quantum technologies requires single-photon nonlinearity, such as single-photon blockade, in solid-state systems. Recently, it has been shown that single-photon Fock states can, in principle, be unconditionally generated using arbitrarily small intrinsic optical nonlinearities in photonic cavities. We investigate the feasibility of such a scheme in achieving photon blockade in an on-chip silicon photonics platform. We show that a triply resonant nanobeam cavity pumped with three monochromatic lasers could achieve such functionalities with quality factors ∼107\sim 10^7∼107 and effective mode volumes ∼10−2μm3\sim 10^{-2} μm^3∼10−2μm3, for experimentally feasible incident powers. Using quantum optical simulations, we propose an experimental protocol to generate single photons under this scheme. The constraints on the cavity design and experimental conditions are thoroughly explored to determine feasible regimes of operation.
An arbitrary initial state of an optical or microwave field in a lossy driven nonlinear cavity can be changed into a partially incoherent superposition of only the vacuum and the single-photon states. This effect is known as single-photon blockade, which is usually analyzed for a Kerr-type nonlinear cavity parametrically driven by a single-photon process assuming single-photon loss mechanisms. We study photon blockade engineering via a nonlinear reservoir, i.e., a quantum reservoir, where only two-photon absorption is allowed. Namely, we analyze a lossy nonlinear cavity parametrically driven by a two-photon process and allowing two-photon loss mechanisms, as described by the master equation derived for a two-photon absorbing reservoir. The nonlinear cavity engineering can be realized by a linear cavity with a tunable two-level system via the Jaynes-Cummings interaction in the dispersive limit. We show that by tuning properly the frequencies of the driving field and the two-level system, the steady state of the cavity field can be the single-photon Fock state or a partially incoherent superposition of several Fock states with photon numbers, e.g., (0,2), (1,3), (0,1,2), or (0,2,4). At the right (now fixed) frequencies, we observe that an arbitrary initial coherent or incoherent superposition of Fock states with an even (odd) number of photons is changed into a partially incoherent superposition of a few Fock states of the same photon-number parity. We find analytically approximate formulas for these two kinds of solutions for several differently tuned systems. A general solution for an arbitrary initial state is a weighted mixture of the above two solutions with even and odd photon numbers, where the weights are given by the probabilities of measuring the even and odd numbers of photons of the initial cavity field, respectively. This can be interpreted as two separate evolution-dissipation channels for even and odd-number states. Thus, in contrast to the standard predictions of photon blockade, we prove that the steady state of the cavity field, in the engineered photon blockade, can depend on its initial state. To make our results more explicit, we analyze photon blockades for some initial infinite-dimensional quantum and classical states via the Wigner and photon-number distributions.
The photon blockade based on weak nonlinearities is called the unconventional photon blockade. The study of the unconventional photon blockade in recent decades has mainly focused on the ${\ensuremath{\chi}}^{(3)}$ Kerr nonlinearity. In this paper, we study the photon blockade in two weakly coupled nonlinear cavities via ${\ensuremath{\chi}}^{(2)}$ nonlinearity, where ${\ensuremath{\chi}}^{(2)}$ mediates the conversion of a single photon in the cavity with high frequency into two photons with low frequency in another cavity. When the two cavity modes are driven simultaneously, our calculations show that the strong photon antibunching can be obtained in the cavity. The optimal condition for strong antibunching is found by analytic calculations and numerical simulations, and discussions of the optimal condition are presented. The differences between the present scheme and that with ${\ensuremath{\chi}}^{(3)}$ nonlinearity are discussed. This scheme is not sensitive to the change of decay rates, which makes the experimental realization easy.
Abstract We propose an unconventional photon blockade scheme in coupled semiconductor microcavities embedded in a nonlinear Kerr medium in the presence of photon leakage and bimodal driving on two cavity modes, which consists of two spatially overlapping single-mode semiconductor cavities with cross-Kerr nonlinearity and two-photon tunneling. A detailed analysis is derived for the exact optimal conditions for strong photon antibunching with weak Kerr nonlinearities. It is very important to find the transition of the structures of the solution for the optimal detuning from the quartic equation to the cubic equation when changing the two complex driving fields appropriately. The transition originates from the second driving field that compensates the numbers of interference paths reaching a two-photon state. This unconventional photon blockade can be realized by coupled photonic crystal cavities filled with a nonlinear Kerr medium. This implies that nonlinear Kerr medium systems can be used to generate tunable single-photon sources by tuning the strength and relative phase of two complex driving fields under weak Kerr nonlinearity.
Abstract In conventional photon blockade, the occupation of a cavity mode by more than one photon is suppressed via strong optical nonlinearity. An alternative, called unconventional photon blockade, can occur under weak nonlinearity by relying on quantum interference between fine-tuned cavities. A serious limitation to this approach is the very short antibunching time window, orders of magnitude less than the cavity lifetime. We present a scheme to achieve photon blockade over a large time window of several cavity lifetimes, even exceeding that of conventional photon blockade, while still requiring only weak nonlinearity. This “long-lived photon blockade” (LLPB) occurs when the single-particle Green’s function exhibits a zero at a large cavity loss rate, which is satisfied by an exemplary configuration of four coupled cavities under weak driving. Our analytical results agree well with wavefunction Monte Carlo simulations. The LLPB phenomenon may aid the development of single-photon sources utilizing materials with weak optical nonlinearities.
In this paper, we show that photon blockade can be observed in a system with weak Kerr nonlinearities. The system consists of two spatially overlapping single-mode semiconductor cavities with tunable one- and two-photon tunneling. We find that both conventional and unconventional single-photon blockades are controllable by manipulating the phase in the hopping regardless of the weakness of nonlinearity. We refer to the photon blockade with weak nonlinearities as an unconventional photon blockade. The unconventional photon blockade effect originates from the destructive interference between different paths from the ground state to two-photon states. We analytically derive the exact optimal conditions for strong antibunching, which are in good agreement with those obtained by numerical simulations. The optimal parameters for photon blockade are derived. Based on these parameters, the semiconductor cavity systems can be used as a single-photon source in regimes of both weak and strong nonlinearities.