Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPerturbative diagonalization for time-dependent strong interactions
80
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a systematic method to implement a perturbative Hamiltonian diagonalization based on the time-dependent Schrieffer-Wolff transformation. Applying our method to strong parametric interactions we show how, even in the dispersive regime, full Rabi model physics is essential to describe the dressed spectrum. Our results unveil several qualitatively new results including realization of large energy-level shifts, tunable in magnitude and sign with the frequency and amplitude of the pump mediating the parametric interaction. Crucially Bloch-Siegert shifts, typically thought to be important only in the ultra-strong or deep-strong coupling regimes, can be rendered large even for weak dispersive interactions to realize points of exact cancellation of dressed shifts (`blind spots) at specific pump frequencies. The framework developed here highlights the rich physics accessible with time-dependent interactions and serves to significantly expand the functionalities for control and readout of strongly-interacting quantum systems.
rate research
Read More
Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-body Hamiltonian up to an absolute error $epsilon$. Typically, gadget constructions involve terms with large interaction strengths of order $text{poly}(epsilon^{-1})$. Here we present a 2-body gadget construction and prove that it approximates a target many-body Hamiltonian of interaction strength $gamma = O(1)$ up to absolute error $epsilonllgamma$ using interactions of strength $O(epsilon)$ instead of the usual inverse polynomial in $epsilon$. A key component in our proof is a new condition for the convergence of the perturbation series, allowing our gadget construction to be applied in parallel on multiple many-body terms. We also show how to apply this gadget construction for approximating 3- and $k$-body Hamiltonians. The price we pay for using much weaker interactions is a large overhead in the number of ancillary qubits, and the number of interaction terms per particle, both of which scale as $O(text{poly}(epsilon^{-1}))$. Our strong-from-weak gadgets have their primary application in complexity theory (QMA hardness of restricted Hamiltonians, a generalized area law counterexample, gap amplification), but could also motivate practical implementations with many weak interactions simulating a much stronger quantum many-body interaction.
We extend the gauge choice problem Lamb noticed to include a time-dependent relativistic non-perturbative Coulomb field, which can be produced by a cluster of relativistic charged particles. If adiabatic conditions are carefully maintained, such a field must be included along side the nuclear Coulomb potential when defining the atomic state. We reveal that when taking the external field approximation, the gauge choice for this time-dependent relativistic non-perturbative Coulomb field cannot be overcome by previous method, and leads to considerable gauge-dependence of the transient spontaneous radiation spectrum. We calculate explicitly with a simple one-dimensional charged harmonic oscillator that such a gauge-dependence can be of a measurable magnitude of 10 MHz or larger for the commonly used Coulomb, Lorentz, and multipolar gauges. Contrary to the popular view, we explain that this gauge dependence is not really a disaster, but actually an advantage here: The relativistic bound-state problem is so complicated that a fully quantum-field method is still lacking, thus the external field approximation cannot be derived and hence not guaranteed. However, by fitting to the experimental data, one may always define an effective external field, which may likely be parameterized with the gauge potential in a particular gauge. This effective external field would not only be of phenomenological use, but also shed light on the physical significance of the gauge field.
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the amplitude level. As a test application, we apply this method to QED and study photon emission from an electron in a strong, time-dependent external field. Coherent superposition of electron acceleration and photon emission is observed in the nonperturbative regime.
We theoretically study specific schemes for performing a fundamental two-qubit quantum gate via controlled atomic collisions by switching microscopic potentials. In particular we calculate the fidelity of a gate operation for a configuration where a potential barrier between two atoms is instantaneously removed and restored after a certain time. Possible implementations could be based on microtraps created by magnetic and electric fields, or potentials induced by laser light.
The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies. Recently, new regimes beyond the weak and strong light-matter coupling have been explored in several settings. These regimes, where the interaction strength is comparable (ultrastrong) or even higher (deep-strong) than the transition frequencies in the system, can give rise to new physical effects and applications. At the same time, they challenge our understanding of cavity QED. When the interaction strength is so high, fundamental issues like the proper definition of subsystems and of their quantum measurements, the structure of light-matter ground states, or the analysis of time-dependent interactions are subject to ambiguities leading to even qualitatively distinct predictions. The resolution of these ambiguities is also important for understanding and designing next-generation quantum devices that will exploit the ultrastrong coupling regime. Here we discuss and provide solutions to these issues.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
