On-chip nonclassical light sources
Fig.1. Left: Ladder of dressed states in a strongly coupled quantum dot-cavity system. Right: The anharmonicity of this ladder can be employed to achieve photon blockade (input laser frequency tuned to first order dressed states - see blue arrow in the left figure), or photon induced tunneling (input laser frequency tuned to higher order dressed states - e.g., 2nd order dressed states, as shown by the red arrow in the left figure).
The goal of this project is to build non-classical light sources on a chip by employing the photon blockade and photon-induced tunneling effects. This is implemented with photonic-crystal nanocavities with embedded quantum dots (QDs) using the effects originating in cavity quantum electrodynamics (cQED). In particular, we are focusing on on-demand, deterministic generation of single photons and multi-photon states. In contrast to the single photon generation schemes based on atom-optics, one does not need complex setups for atom cooling and trapping, as everything is done in an integrated structure fabricated on a chip using processes compatible with semiconductor manufacturing.
In the most basic scheme (Fig.1), the non-classical light is generated by filtering a stream of photons coming from a classical coherent light source producing photons with Poisson statistics through a single photonic-crystal nano-cavity containing a single, strongly coupled QD. Due to the highly nonlinear character of the interaction between the input light and a strongly coupled cavity-QD system, the output light can be engineered into a stream of single photons. Furthermore, higher order photon states (consisting of, e.g., two or three photons), can be preferentially generated by tuning the frequency of the input light (Fig 2.) . A source of such higher order photon states, also known as Fock states, can then be used for efficient generation of NOON-states. These large entangled photon states are particularly interesting for quantum metrology and high resolution quantum lithography and sensing.
Beyond studies based on a simple cavity with a QD, we explore cQED and non-classical light generation in more complex systems, such as photonic molecules (Fig. 3) , bimodal nanocavities (Fig. 4) , and large systems of coupled cavities.
Fig. 2: Numerically calculated photon statistics at the output of the QD-cavity system driven by Gaussian pulses with duration τp ~ 24 ps. The simulation parameters are g=2p×40GHz, κ=2p×4GHz, and Eo =2p×9GHz; pure QD dephasing is neglected. (a) P(n), probability of generating an n photon state at the cQED system output as a function of laser-cavity detuning Δc. (b) The ratios r1 and r2 (probabilities of generating one and two photon states relative to other photon states -- see text for details) as a function of Δc in our system. The dotted lines show the expected values of the ratios from a classical coherent state. (c) Second order auto-correlation g(2)(0) as a function of Δc. The red dashed line shows the expected g(2)(0) for a coherent state. (d) Second order differential correlation C(2)(0) as a function of Δc. (e) C(2)(0) as a function of the laser-cavity detuning Δc for different values of the peak laser field Eo/2p (in units of GHz). We observe that the peak in the C(2)(0) occurs at Δc = 0.7g for weaker excitation (where the second order manifold is excited resonantly via two photons). However, with increasing excitation power, the peak positions shifts towards Δc = 0, due to excitation of higher manifolds.
Fig. 3: QD-photonic molecule spectrum, (a) when the QD is resonant with super-mode sm2 and (b) when the QD is resonant with super-mode sm1. From the fit we extract the system parameters, including the cavity-cavity and dot-cavity coupling strengths. (c) Numerically simulated second order autocorrelation g(2)(0) (top) and transmission (bottom) from cavity b, as a function of laser frequency, with the experimental system parameters that were extracted from the fits. (d) An SEM image of the photonic molecule consisting of two cavities coupled by proximity coupling. (e) Off-resonant interaction between two coupled cavities and a QD. We scan the laser across both coupled modes, and observe emission from the QD and the offresonant super-mode, under excitation of the other super-mode. A close-up spectrum for each resonance shows the relative position of the laser and the cavity modes.
Fig. 4: (a) Schematics of the sub-Poissonian light generation with a QD coupled to a bimodal cavity. (b) Scanning electron microscope (SEM) image of a fabricated bimodal cavity (H1 design based on omitting a single hole from the photonic crystal). g(2)(0) as a function of (c) the frequency mismatch Δab between the two modes of the cavity for various values of the cavity decay κ, and (d) the mismatch between the Rabi frequencies associated with each of the modes. (e) Second order autocorrelation g(2)(0) for the conventional photon blockade in a single mode cavity as a function of the QD-cavity coupling strength g and cavity field decay rate κ. g(2)(0) decreases with increasing value of g/κ, as expected, as a result of reduced overlap of energy eigenstates in the anharmonic ladder. (f) g(2)(0) for the bimodal cavity as a function of g and κ. g(2)(0)is calculated for the output of mode a, i.e., for photons leaking from the mode a. We observe that g(2)(0) → 1 (Poissonian output) when g/κ → 0 or ∞. However, we can observe very low g(2)(0) even when the QD is not strongly coupled to the two cavity modes (g < κ/2). (g) g(2) (0) as a function of the ratio κ/g for different g showing sub-Poissonian light generation in the
bimodal cavity even in the weak coupling regime.
- A. Majumdar, M. Bajcsy, J. Vuckovic, Probing the ladder of dressed states and non-classical light generation in quantum-dot-cavity QED, Phys. Rev. A (Rapid Comm.), 041801(2012)
- A. Majumdar, A. Rundquist, M. Bajcsy, J. Vuckovic, Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule, Phys. Rev. B (accepted), arXiv: 12016244
- A. Majumdar, M. Bajcsy, A. Rundquist, J. Vuckovic, Loss-enabled photon blockade and sub-Poissonian light generation in a bimodal nanocavity, Phys. Rev. Letters 108, 183601 (2012)
last modified on Wednesday September 05, 2012