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 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.
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 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 study the near-resonant dipole-dipole interaction between two atoms in a broadband squeezed vacuum. We show that this ``vacuum'' modifies the rate of spontaneous emission of the atoms so that it may depend not merely on their relative position, as is normally the case, but also on their center-of-mass position. The explicit form of this latter dependence is a function of the way squeezing is achieved. We also show that in contrast to the spontaneous decay rate, squeezed vacua do not modify the dipole-dipole potential between the atoms as compared to its usual form. Finally, we develop a Monte Carlo wave-function description of the interaction between atoms with an arbitrary internal structure and a squeezed vacuum and apply this formalism to the case of off-resonant excitation of the atoms. We find that in addition to the usual light shift, the squeezed vacuum results in an additional contribution to the effective potential governing the evolution of the atomic ground states. \textcopyright{} 1996 The American Physical Society.
The interaction of an atomic two-level system and a squeezed vacuum leads to interesting effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of-phase components of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a $4\ensuremath{\pi}$ squeezed vacuum. In this paper we show how to ``engineer'' a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two-level atom is represented by the two ground levels of an atom with an angular momentum $J=1/\stackrel{\ensuremath{\rightarrow}}{2}J=1/2$ transition (a four-level system), which is driven by (weak) laser fields and coupled to the vacuum reservoir of radiation modes. Interference between the spontaneous emission channels in optical pumping leads to a squeezed-bath-type coupling and thus to symmetry breaking of decay on the Bloch sphere. With this system it should be possible to observe the effects predicted in the context of squeezed-bath--atom interactions. The laser parameters allow one to choose properties of the squeezed-bath interaction, such as the (effective) photon-number expectation number N and the squeezing phase $\ensuremath{\varphi}$. We present results of a detailed analytical and numerical study.
Waveguide quantum electrodynamics (waveguide QED) describes the interaction between an electromagnetic field confined to a one-dimensional waveguide with atom-like quantum emitters close by. The characteristics of these kinds of systems are the possibility for strong and even ultrastrong interactions between the photonic and atom-like systems, and practically infinite range interactions between the emitters. These properties are valuable for a wide range of quantum optical applications, like quantum communication, quantum networks and quantum metrology. In this thesis we focus on two challenges in quantum optics, namely the generation and scattering of multiphoton states. In the first part of this thesis we demonstrate how waveguide QED systems can be exploited for the generation of multiphoton states, in particular of single-mode Fock states and superpositions thereof as well as multi-mode photonic states with metrological applications. The basic setup for this goal is an ensemble of quantum emitters coupled to a waveguide. In the so-called atomic mirror configuration symmetric Dicke states (or a superposition thereof) decay superradiantly to the ground state and emit the desired multiphoton state, which can be efficiently collected at the ends of the waveguide. We propose various protocols for the preparation of these Dicke states in waveguide QED systems and characterize the emitted photonic state. It turns out that in the low excitation regime, that is, if the number of photons is much lower than the ensemble size, the photonic state is emitted into a single mode. This single-mode structure is fundamental to current proposals for applications in quantum metrology with optical interferometers. Outside the low excitation regime, a multi-mode photonic state is generated, for which the metrological capabilities were unknown. We were able to show that these states still lead to quantum-enhanced optical interferometry. In the second part of this thesis we demonstrate how the scattering of multiphoton states on a single quantum emitter coupled to the waveguide can be used for testing the limits of the light-matter interaction strength. In particular, we investigate systems in the so-called ultrastrong coupling regime, where the coupling strength between the photonic and atom-like system is of the order of the emitter's transition energy. In this regime, many methods and approximations used in quantum optics, especially the Rotating Wave Approximation, break down and one needs to develop new analytical and numerical methods to study these systems. One approach is the so-called polaron Transformation. We show how this transformation can be applied for predicting the scattering amplitude of few photons scattering on the emitter. The comparison of these results with numerical simulations using matrix product states shows a good agreement for moderate coupling strengths. Both parts together show that waveguide QED systems are promising candidates for the generation of multiphoton states as well as for the investigation of fundamental limits probed through the scattering of multiphoton states. The latter also finds application in the implementation of photon-photon nonlinearities induced by the interaction with the quantum emitters. Apart from these and many other theoretical predictions, waveguide QED systems are also undergoing rapid progress in experiments. Therefore, we expect these kinds of systems to bring forth several advances in the field of quantum optics.
Waveguide circuit quantum electrodynamics (waveguide circuit QED) studies light-matter interaction with superconducting circuits in one dimension. In circuit QED, natural atoms are replaced by superconducting qubits consisting of a non-linear Josephson junction, resulting in an anharmonic energy spectrum just like real atoms. With superconducting qubits, it is possible to study quantum optical phenomena and reach new regimes hard to achieve with real atoms due to weak coupling to the electromagnetic field. The reduction to one dimension in waveguide QED increases the electromagnetic field's directionality, which results in reduced losses. In this thesis, we first introduce circuit quantisation, giving the basis for the next part, where we investigate a transmon, a charge-insensitive artificial atom, coupled to a semi-infinite transmission line. An atom coupled to a semi-infinite waveguide is referred to as an atom in front of a mirror and is the subject of all appended papers. We proceed by summarising Paper I and III's main results: in Paper I, we investigate the spontaneous emission of a transmon coupled to a semi-infinite transmission line, where we take time-delay effects into account. We find that the system dynamics strongly depend on the coupling strength to the transmission line and the atom's position with respect to the electromagnetic field, leading to the Purcell effect or the convergence to a dark state with finite excitation probability. In the high-impedance regime, which we investigate in Paper III, the properties of the transmon coupled to the high-impedance transmission line change drastically. It becomes highly reflective and creates its own cavity with the mirror, resulting in the emergence of cavity modes and vacuum Rabi oscillations in the spontaneous emission dynamics. In the next chapter of the thesis, we demonstrate how to quantise an electromagnetic field and derive a light-matter interaction Hamiltonian within dipole approximation. We then give an introduction to open quantum systems and derive the quantum-optical master equation in Lindblad form. Furthermore, we introduce the dressed state picture, where the interaction of light and matter is so strong that the individual energy levels of light and matter are no longer separable. Both the quantum optical master equation and the dressed state picture are relevant in Paper II and IV. In Paper II, an experimental collaboration, we perform several experiments to characterise and discriminate different decay rates of a superconducting qubit coupled to the end of a transmission line. One experiment measured the atomic fluorescence spectral density, which shows an asymmetry for off-resonant driving, resulting from pure dephasing: an effect that we explain in more detail in this thesis and Paper II. In Paper IV, we theoretically investigate amplification mechanisms realised by different set-ups of an atom coupled to a semi-infinite waveguide. In the considered systems, the amplification of a probe field happens either due to population inversion between the pure states or dressed states or multi-photon processes. We find that compared to an open waveguide, we can achieve a higher gain in the amplification with a semi-infinite waveguide.