Mitchell Physics Building
College Station, Texas 77843-4242
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
Photon transport in a waveguide system coupled to quantum emitters, well known as "waveguide-QED", has attracted extensive interests because of its possible applications in quantum device and quantum information. The stationary photon spectrum can be calculated by various methods such as the Bethe ansatz approach , Lippmann-Schwinger scattering theory , and the input-output theory . Recently, we derived a dynamical theory to study a single-photon transport in the waveguide-QED system which allows us to calculate the real-time evolution of the emitters and photon pulse [4-7]. In this presentation, I will talk about the stationary and dynamical theories for calculating photon transport in the waveguide-QED system. I will also briefly talk about some possible applications of this system.
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