Quantum state tomography aims to reconstruct the quantum state of a system, including its phase and coherence information. In electron tomography experiments, the reconstructed object is understood as the quantum state of the electron. However, for charged particles, the bare electron state is gauge dependent:
ψ(x)→eieΛ(x)/ℏψ(x). This raises a fundamental question: how can an experiment reconstruct a gauge-dependent quantum state? One possible resolution is that tomography does not reconstruct the bare electron state but instead a gauge-invariant dressed electron state,
ΨD=W[A]ψ, where the electromagnetic dressing compensates the gauge transformation of the electron field. In this paper, we examine this alternative possibility and show that it is not viable. We prove a structural no-go theorem showing that measurement interactions generated by the QED current coupling cannot directly measure a gauge-invariant dressed electron state. We further show that although interpreting tomography as the reconstruction of the reduced electron state of a dressed electron is possible, the dressed-electron interpretation fails in the Aharonov--Bohm effect: the dressed formalism can reproduce the observed phase only as a mathematical redefinition, not as a physically dynamical mechanism. Consequently, the quantum state reconstructed in electron tomography is indeed the bare electron state, as assumed in the standard interpretation of these experiments. The experimental reconstruction of this gauge-dependent quantum state implies that the electromagnetic potential entering the quantum dynamics cannot be regarded as merely a conventional mathematical artifact. Rather, it must correspond to a real physical configuration uniquely determined by the complete physical laws governing the electromagnetic field, such as Maxwell's equations together with the Lorenz condition, and by the appropriate boundary and causal conditions. This provides empirical support for the reality of the electromagnetic potential
Aμ. The same reasoning suggests an analogous conclusion for gravity, where the reconstruction of bare quantum states supports the reality of the gravitational field
gμν.
Microscopic and macroscopic descriptions of electromagnetic-field propagation relevant to resonant pumpprobe optical phenomena, such as electromagnetically induced transparency, in quantized many-electron systems are formulated within the framework of a general reduced-density-matrix approach. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified and self-consistent manner. A semiclassical perturbation-theory treatment of the electromagnetic interaction is adopted, in which the electromagnetic field is described as a classical field satisfying either the microscopic form or the macroscopic form of the Maxwell equations. However, it is emphasized that a quantized-field approach is essential for a fully self-consistent quantummechanical formulation. Compact Liouville-space operator expressions are obtained for the linear and the general (n'th order) non-linear electromagnetic-response tensors for moving many-electron systems. These expressions can be evaluated for coherent initial electronic excitations and for the full tetradic-matrix form of the Liouville-space selfenergy operator in the Markov (short-memory-time) approximation. Environmental interactions can be treated in terms of the Liouville-space self-energy operator, and the influence of Zeeman coherences on electromagnetic-field propagation can be investigated by including an applied magnetic field together with the electromagnetic field.
Non-linear interactions involving pump-probe optical phenomena, such as electromagnetically induced transparency, in quantized many-electron systems are investigated using a reduced-density-matrix approach. Time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are developed in a unified manner and self-consistent manner. The standard Born (lowest-order perturbation-theory) and Markov (short-memory-time) approximations are systematically introduced within the framework of the general non-perturbative and non-Markovian formulations. A preliminary semiclassical perturbation-theory treatment of the electromagnetic interaction is adopted. However, it is emphasized that a quantized-electromagnetic-field approach is essential for a self-consistent quantum-mechanical formulation. Our primary result is the derivation of compact Liouville-space operator expressions for the linear and the general (n'th order) non-linear macroscopic electromagnetic-response tensors for moving many-electron system. These expressions can be evaluated for coherent initial electronic excitations and for the full tetradic-matrix form of the Liouville-space self-energy operator representing the environmental interactions in the Markov approximation. Environmental interactions can be treated in various approximations for the self-energy operator, and the influence of Zeeman coherences on electromagnetic-field propagation can be investigated by including an applied magnetic field on an equal footing with the electromagnetic fields.