Cavity-Free Photon Blockade Induced by Many-Body Bound States

The manipulation of individual, mobile quanta is a key goal of quantum communication; to achieve this, nonlinear phenomena in open systems can play a critical role. We show theoretically that a variety of strong quantum nonlinear phenomena occur in a completely open one-dimensional waveguide coupled to an $N$-type four-level system. We focus on photon blockade and the creation of single-photon states in the absence of a cavity. Many-body bound states appear due to the strong photon-photon correlation mediated by the four-level system. These bound states cause photon blockade, which can generate a sub-Poissonian single-photon source.

Figure 1

Schematic diagram of the waveguide system and EIT. (a) $N$-type four-level system interacting with the waveguide continuum. The transitions $|1⟩\leftrightarrow |2⟩$ and $|3⟩\leftrightarrow |4⟩$ are coupled to the waveguide modes with strength $V$ and detuning $\delta$. The transition $|2⟩\leftrightarrow |3⟩$ is driven by a semiclassical control field with Rabi frequency $\Omega$ and detuning $\Delta$. Here, $\omega$ and ${\omega }_c$ are the frequencies of the incoming photons and the control field. (b) Schematic of a possible experimental setup based on superconducting charge qubits [24]. Two charge qubits, each formed from two Josephson junctions [dark gray (green) regions], are coupled capacitively to each other and to a transmission line (1D waveguide). (c) Single-photon transmission probability as a function of incident photon detuning. EIT occurs when the control field is on ($\Omega =1.6$, solid); when it is off, the 4LS becomes a two-level system and EIT disappears. Here, the effective Purcell factor is $P=6$.

Figure 2

Photon blockade in transmission. (a) Photon blockade strengths $P_{21}$ (solid line) and $P_{31}$ (dashed line) as functions of the decay rate $\Gamma$ into the waveguide modes (photon blockade is strongest when $P_{21}$ is smallest). The photons are on resonance with the 4LS ($\delta =0$), and $\Omega =1.6$. Strong coupling produces substantial photon blockade, despite EIT being present in the single-photon properties. (b) $P_{21}$ and $P_{31}$ as functions of the incident photon detuning $\delta$ for $\Gamma =6$ and $\Omega =1.6$. There is clear photon blockade on resonance, as well as photon-induced tunneling ($P_{21},P_{31}>1$) on the sides of the resonance.

Figure 3

Many-body bound-state effect causing photon blockade. (a) Transmission as a function of the decay rate $\Gamma$ into the waveguide modes for $\Omega =1.6$. The presence of the many-body bound states suppresses the multiphoton transmission. (b) Transmission as a function of incident photon detuning $\delta$ for $\Gamma =6$ and $\Omega =1.6$. The bound states strikingly oppose multiphoton EIT; off resonance, their constructive interference produces photon-induced tunneling.

Figure 4

Nonclassical photon states. Photon-number statistics quantified by ${log}_{10}(P_n/P_{n,\mathrm{Poisson}})$, where the probability of $n$ photons in the output state is $P_n$ and $P_{n,\mathrm{Poisson}}$ is for a coherent state with the same mean photon number. Panels (a)–(d) show results for $n=0$, 1, 2, and 3, respectively, as functions of the control field strength $\Omega$ and the decay rate $\Gamma$. The dashed line is a guide to the eye indicating equal probabilities, $P_n/P_{n,\mathrm{Poisson}}=1$. Note the large range of parameters for which the single-photon probability is enhanced while the multiphoton content is suppressed—an improved single-photon source.