Activating transitions between internal states of physical systems has emerged as an appealing approach to create lattices and complex networks. In such a scheme, the internal states or modes of a physical system are regarded as lattice sites or network nodes in an abstract space whose dimensionality may exceed the systems’ apparent (geometric) dimensionality. This introduces the notion of synthetic dimensions, thus providing entirely novel pathways for fundamental research and applications. Here, we analytically show that the propagation of multiphoton states through multiport waveguide arrays gives rise to synthetic dimensions where a single waveguide system generates a multitude of synthetic lattices. Since these synthetic lattices exist in photon-number space, we introduce the concept of pseudo-energy and demonstrate its utility for studying multiphoton interference processes. Specifically, the spectrum of the associated pseudo-energy operator generates a unique ordering of the relevant states. Together with generalized pseudo-energy ladder operators, this allows for representing the dynamics of multiphoton states by way of pseudo-energy term diagrams that are associated with a synthetic atom. As a result, the pseudo-energy representation leads to concise analytical expressions for the eigensystem of N photons propagating through M nearest-neighbor coupled waveguides. In the regime where N ≥ 2 and M ≥ 3 , nonlocal coupling in Fock space gives rise to hitherto unknown all-optical dark states that display intriguing nontrivial dynamics.
Activating transitions between internal states of physical systems has emerged as an appealing approach to create lattices and complex networks. In such a scheme, the internal states or modes of a physical system are regarded as lattice sites or network nodes in an abstract space whose dimensionality may exceed the systems’ apparent (geometric) dimensionality. This introduces the notion of synthetic dimensions, thus providing entirely novel pathways for fundamental research and applications. Here, we analytically show that the propagation of multiphoton states through multiport waveguide arrays gives rise to synthetic dimensions where a single waveguide system generates a multitude of synthetic lattices. Since these synthetic lattices exist in photon-number space, we introduce the concept of pseudo-energy and demonstrate its utility for studying multiphoton interference processes. Specifically, the spectrum of the associated pseudo-energy operator generates a unique ordering of the relevant states. Together with generalized pseudo-energy ladder operators, this allows for representing the dynamics of multiphoton states by way of pseudo-energy term diagrams that are associated with a synthetic atom. As a result, the pseudo-energy representation leads to concise analytical expressions for the eigensystem of N photons propagating through M nearest-neighbor coupled waveguides. In the regime where N ≥ 2 and M ≥ 3 , nonlocal coupling in Fock space gives rise to hitherto unknown all-optical dark states that display intriguing nontrivial dynamics.
Indistinguishable and/or entangled photons propagating in waveguide arrays (WAs) represent a promising platform whose utility ranges from research on fundamental aspects of quantum mechanics all the way to applications in quantum sensing and quantum information processing. Quantum simulators of decoherence reveal that while decoherence processes inevitably destroy single-particle coherence and any form of multiparticle entanglement, quantum correlations based on particle indistinguishability do endure. Further, by judiciously combining multi-photon states with the idea of synthetic dimensions in WAs yields the notion of a synthetic atom and in turn this provides entirely novel perspectives on the dynamics of such multi-photon states. Similarly, simple beam splitters fed with indistinguishable photons, can be used to perform discrete fractional Fourier transforms or can be tuned to realize exceptional points of any order. The latter setup facilitates efficient quantum-enhanced sensors.
Fock-state lattices (FSLs) are becoming an emerging research hotspot in quantum physics, not only because the FSLs provide a new perspective for studying atom-field interactions, but also because they build a connection between quantum optics and condensed matter physics. Because of the multiple transition paths in the lattices, an inherent quantum interference effect exists in these systems, and hence finding new quantum-coherent phenomena and exploiting their applications become a significant and desired task in this field. In this work, we study the dark-state effect in the FSLs generated by the multimode Jaynes-Cummings (JC) models. By considering the FSLs in certain excitation-number subspaces, we study the dark states with respect to the states associated with the atomic excited state using the arrowhead-matrix method. We find that dark-state subspaces exist with dimensions determined by the number of orthogonal dark states. When the dimension is greater than one, the forms of these dark-state bases are not unique. Further, we obtain the number and form of the orthogonal dark states in the two-, three-, and four-mode JC models. In addition, we find that for a general N -mode JC model, there are C N + n − 2 N − 2 orthogonal dark states in the n -excitation subspace. We also build the relationship between the dark states and dark modes. Our work paves the way for exploring quantum optical effects and quantum information processing based on the FSLs.
In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems. Thus, contrary to the common setting where the walker resides in real space or phase space, here the walk takes place in a synthetic space. We present a general formalism based on Lie algebras and their properties. For each Lie algebra one can associate both a phase space and a Fock-state lattice, and by understanding how these spaces are related, together with the action of generalized displacement operators, we construct the discrete unitary operator that generates the walk. In this framework the displacement operators replace the usual nearest-neighbor shifts and lead to state-dependent tunneling on the lattice. By considering several examples we demonstrate ballistic spreading and other characteristic features of discrete-time quantum walks, such as coin-walker entanglement and symmetry-induced interference patterns. We also show that different algebraic structures can give rise to qualitatively different dynamics, including anomalous behavior such as super-ballistic spreading as well as localization effects.
Synthetic dimensions are powerful tools for quantum simulation and computation. They are realized by harnessing internal or external degrees of freedom of an atom or molecule, which can mimic the motion of an electron in a real-space lattice potential. Such degrees of freedom are highly tunable and can be engineered to create configurations difficult to access or realize in real space. Some of the exciting possibilities include realizing higher dimensions systems[1, 2, 3], nontrivial real space[4, 5] and band structure[6, 7] topologies and artificial gauge fields[8, 9]. Experiments have utilized various degrees of freedom to create synthetic dimensions, such as motional[10, 11], spin[8, 12, 13, 14] and rotational[15] levels of atoms and molecules, and frequency modes, spatial modes, and arrival times in photonic systems[16]. Atomic synthetic dimensions have demonstrated artificial gauge fields, spin-orbit coupling, chiral edge states using Raman-coupled ground magnetic sublevels[8, 12, 17] of atoms, and phenomena such as Anderson localization using two-photon Bragg transitions by coupling free-particle momentum states[18]. Here, we harness the Rydberg levels of 84Sr to realize a synthetic lattice for studying quantum matter. Resonant millimeter-wave (mm-wave) radiation coupling Rydberg levels |i⟩ and |j⟩ with amplitude Ωij (Rabi frequency) are described by the same Hamiltonian as a particle tunneling between lattice sites |i⟩ and |j⟩ with tunneling amplitude Jij = Ωij /2. The mathematical equivalence to particles moving in a real-space lattice enables Rydberg levels to function as a synthetic spatial dimension. Rydberg-atom synthetic dimensions offer control over connectivity, tunneling rates and on-site potentials, which allows for the creation of a broad range of synthetic dimensional system. The capabilities of such a system are demonstrated by realizing the famous Su-Schrieffer-Heeger (SSH) model[19] and studying its topologically protected edge states(TPS).
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.