We study the dynamics of a general multiemitter system coupled to the squeezed vacuum reservoir and derive a master equation for this system based on the Weisskopf-Wigner approximation. In this theory, we include the effect of positions of the squeezing sources which is usually neglected in the previous studies. We apply this theory to a quasi-one-dimensional waveguide case where the squeezing in one dimension is experimentally achievable. We show that while dipole-dipole interaction induced by ordinary vacuum depends on the emitter separation, the two-photon process due to the squeezed vacuum depends on the positions of the emitters with respect to the squeezing sources. The dephasing rate, decay rate, and the resonance fluorescence of the waveguide-QED in the squeezed vacuum are controllable by changing the positions of emitters. Furthermore, we demonstrate that the stationary maximum entangled NOON state for identical emitters can be reached with arbitrary initial state when the center-of-mass position of the emitters satisfies certain conditions.
We study the dynamics of a general multiemitter system coupled to the squeezed vacuum reservoir and derive a master equation for this system based on the Weisskopf-Wigner approximation. In this theory, we include the effect of positions of the squeezing sources which is usually neglected in the previous studies. We apply this theory to a quasi-one-dimensional waveguide case where the squeezing in one dimension is experimentally achievable. We show that while dipole-dipole interaction induced by ordinary vacuum depends on the emitter separation, the two-photon process due to the squeezed vacuum depends on the positions of the emitters with respect to the squeezing sources. The dephasing rate, decay rate, and the resonance fluorescence of the waveguide-QED in the squeezed vacuum are controllable by changing the positions of emitters. Furthermore, we demonstrate that the stationary maximum entangled NOON state for identical emitters can be reached with arbitrary initial state when the center-of-mass position of the emitters satisfies certain conditions.
The well-known Purcell effect shows that the spontaneous decay rate of an emitter can be affected by the electromagnetic environment with which the emitters interact. One of the most famous and popular examples is the squeezed vacuum. Although the squeezed vacuum does not change the density of states of the electromagnetic modes, it can modify the decay rate as well as the dephasing rate of the emitters. The interaction between a single atom and the squeezed vacuum has been widely studied, while only a few publications deal with the multiple-atom system. Despite the fact that the dipole-dipole interaction induced by ordinary vacuum depends on the relative separation of atoms, there are only a few papers studying the impact of atomic separation in the squeezed vacuum. In this dissertation, we show that the interaction induced by the squeezed vacuum depends on the center of mass positions of the atoms, which is essentially different from that in the ordinary vacuum. We also illustrate how to choose the coordinate system to make the center of mass position reasonable and well-defined.\n \nAlthough the squeezed vacuum theory has been widely studied, it is impractical to generate a broadband squeezed vacuum reservoir which squeezes all modes in the 3-dimensional (3D) space. Recently, photon transport in a one-dimensional (1D) waveguide coupled to quantum emitters (well known as "waveguide-QED") has attracted much attention due to its possible applications in quantum device and quantum information. In contrast to the 3D case, squeezing in 1D is more experimentally feasible. Suppression of the spontaneous decay rate and the linewidth of the resonance fluorescence atom has been experimentally demonstrated in a 1D microwave transmission line coupled to a single artificial atom. However many-body interaction in a 1D waveguide QED system coupled to the squeezed vacuum has still not yet been studied. In this dissertation, we apply our theory to the 1D waveguide-QED system with the squeezed reservoir. Contrary to the traditional result that the dephasing rate of a single atom is a constant, our calculation shows that the dephasing rate is actually position-dependent. As the dipole-dipole interaction is involved in the atomic system, both the atomic separation and center of mass position have impacts on the decay rate, dephasing rate, and the emitted resonance fluorescence spectrum. Moreover, the stationary maximum entangled NOON state can be achieved if atomic transition frequency is resonant with the center frequency of the squeezed vacuum.\n \nIn light of the fact that two qubits can be treated as a whole to be a four level atomic system, we also study the dynamics of Ξ-type atoms driven by a squeezed vacuum. We get the interesting result that the atomic system’s steady state is a pure state, and a complete population inversion can occur when the coupling between the atomic dipole and the squeezed vacuum satisfy some certain conditions. We also mathematically prove that the steady state of a many-body system is nothing else but the direct product of that in the single atom case even when dipole-dipole interaction is involved.
The study of atomic behaviors in a squeezed vacuum reservoir plays an important role in exploring quantum effect and quantum physics. We here propose a scheme to manipulate the dynamics of giant atoms coupled to a one-dimensional waveguide driven by a broadband squeezed field, which acts as a squeezed vacuum reservoir. By tuning the propagating phase of photons, the center-of-mass phase of the giant atom, and the squeezing parameter, both the dephasing dynamics and entanglement dynamics of giant atoms can be effectively controlled. In the single-giant-atom case, we obtain the expressions of the dephasing rates based on the Bloch equations derived from the quantum master equation of the giant atom. Adjusting these two phases enables the dephasing rates to be enhanced, suppressed, or reduced to zero, thereby changing the dephasing dynamics. For the two-giant-atom system, we find that the atomic individual and collective squeezing depend on these two phases simultaneously. The steady-state giant-atom population and entanglement are obtained by working in the collective state representation for the two atoms. Different from small atoms, the steady-state population and entanglement depend on not only the center-mass-of phase, but also the propagating phase. In addition, we identify the condition for achieving larger steady-state entanglement via analyzing the system parameters. This work will facilitate the study of light-matter interaction based on giant-atom waveguide QED systems driven by a squeezed vacuum reservoir and has potential applications in quantum information processing.
We develop a general dynamical theory for studying a single-photon transport in a one-dimensional (1D) waveguide coupled to multiple emitters which can be either identical or nonidentical. In this theory, both the effects of the waveguide and non-waveguide vacuum modes are included. This theory enables us to investigate the propagation of an emitter excitation or an arbitrary single-photon pulse along an array of emitters coupled to a 1D waveguide. The dipole-dipole interaction induced by the non-waveguide modes, which is usually neglected in the literature, can significantly modify the dynamics of the emitter system as well as the characteristics of the output field if the emitter separation is much smaller than the resonance wavelength. Nonidentical emitters can also strongly couple to each other if their energy difference is less than or of the order of the dipole-dipole energy shift. Interestingly, if their energy difference is close but nonzero, a very narrow transparency window around the resonance frequency can appear which does not occur for identical emitters. This phenomenon may find important applications in quantum waveguide devices such as optical switches and ultranarrow single-photon frequency comb generator.
Quantum emitters coupled to nonlinear one-dimensional waveguides provide a route for quantum-state engineering by utilizing parametric gain accumulation along with modified waveguide-mediated interactions. Since the accumulated squeezing depends on propagation distance, different emitter separations can experience different effective gain, making the spatial structure of connected quantum correlations a central feature of the dynamics. Here we investigate the transient and steady-state connected correlations of emitter arrays coupled to a parametrically driven waveguide. Using an effective master equation for nonlinear waveguide QED, we analyze second- and third-order connected correlations as functions of the squeezing parameter and interparticle distance. In the two-emitter limit, accumulated squeezing drives excitation buildup and generates a nonzero connected second-order correlation. For many-emitter arrays, tuning the interparticle distance switches the dominant local second-order correlation between the bulk and boundary regions, and enables an analogous spatial control of genuine third-order connected correlations. In the steady state, the averaged second-order correlation exhibits sign-changing and nonmonotonic behavior in the squeezing--interparticle distance parameter space, whereas the third-order connected correlation is strongly enhanced by increasing the squeezing parameter. These results identify nonlinear waveguide QED as a tunable platform for spatially controlling connected quantum correlations and provide insights into correlation engineering in open quantum optical arrays. We further show that this local contrast remains visible in both odd and even number of atomic arrays.
We derive a generalized master equation for multiphoton pulses interacting with multiple emitters in a waveguide-quantum electrodynamics system where the emitter frequency can be modulated and the effects of nonguided modes can also be considered. Based on this theory, we can calculate the real-time dynamics of an array of interacting emitters driven by an incident photon pulse which can be vacuum, a coherent state, a Fock state, or their superpositions. Moreover, we also derive generalized input-output relations to calculate the reflectivity and transmissivity of this system. We can also calculate the output photon pulse shapes. Our theory can find important applications in the study of waveguide-based quantum systems.
The possibilities and perspectives of squeezed-light emission are studied for coherently driven single-photon sources, such as atoms and quantum dots. Maximal squeezing is realized, if the electronic subsystem of the emitter is in a pure quantum state. The purification is achieved by using a cavity as a second decay channel, aside from the incoherent coupling to the electromagnetic vacuum. For realistic cavities, this yields a purity of the electronic state of more than 99%. Aside from numerical calculations, we also derive approximate analytical results. Based on the approximations, effects are studied which originate from the environment of the emitter, including radiationless dephasing and incoherent pumping of the emitter and the cavity mode. The fragility of squeezing against decoherence is substantially reduced, so that squeezing persists even under hostile conditions. The measurement of squeezing from such light sources is also considered.