We study the radiation damping and the spin noise of a magnetic material coupled with a resonant circuit.Radiation damping in magnetic resonance is a dissipation phenomenon, where magnetization prepared after a Rabi pulse decays toward its equilibrium state.The magnetic sample loses its energy by the coupling with resonant circuit, that must be tuned in Larmor frequency of the sample spins.Even though this phenomenon had been studied many years ago, no full quantum description was done.We present a quantum Hamiltonian model, that explains the radiation damping.We use quantum Langevin equation method for this task.Beyond radiation damping, we show the magnetization acquires an unusual intrincate motion, if the circuit initial state is coherent.Using the same Langevin equation, we study the sample inuence on the resonant circuit noise.We calculate the current spectral density in the case of thermal equilibrium of whole system.We can verify the method eectiveness, comparing former papers.Moreover we study modications in the circuit noise, if an external oscillating tension is applied.In this situation, other two peaks emerge in the central peak sidebands of the sample absorption spectrum.It leads to appear three dips in circuit current spectrum.This eect is due to the splitting of the spin energy states.We comment about the analogy between this phenomenon and the resonance uorescence in Quantum Optics.
We study the radiation damping and the spin noise of a magnetic material coupled with a resonant circuit.Radiation damping in magnetic resonance is a dissipation phenomenon, where magnetization prepared after a Rabi pulse decays toward its equilibrium state.The magnetic sample loses its energy by the coupling with resonant circuit, that must be tuned in Larmor frequency of the sample spins.Even though this phenomenon had been studied many years ago, no full quantum description was done.We present a quantum Hamiltonian model, that explains the radiation damping.We use quantum Langevin equation method for this task.Beyond radiation damping, we show the magnetization acquires an unusual intrincate motion, if the circuit initial state is coherent.Using the same Langevin equation, we study the sample inuence on the resonant circuit noise.We calculate the current spectral density in the case of thermal equilibrium of whole system.We can verify the method eectiveness, comparing former papers.Moreover we study modications in the circuit noise, if an external oscillating tension is applied.In this situation, other two peaks emerge in the central peak sidebands of the sample absorption spectrum.It leads to appear three dips in circuit current spectrum.This eect is due to the splitting of the spin energy states.We comment about the analogy between this phenomenon and the resonance uorescence in Quantum Optics.
We apply the methods of cavity quantum electrodynamics (CQED), to obtain a microscopic and fully quantum-mechanical picture of radiation damping in magnetic resonance, and the nascent formation of the free induction signal. Numerical solution of the Tavis-Cummings model - i.e., multiple spins 1∕2 coupled to a lossless single-mode cavity - shows in fine detail the transfer of Zeeman energy, via spin coherence, to excite the cavity - represented here by a quantized LC resonator. The case of a single spin is also solved analytically. Although the motion of the Bloch vector is non-classical, we nonetheless show that the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission) gives realistic estimates of macroscopic signal strength and the radiation damping constant in nuclear magnetic resonance. We also show how to introduce dissipation: cavity losses by means of a master equation, and relaxation by the phenomenological method of Bloch. The failure to obtain the full Bloch equations (unless semi-classical conditions are imposed on the cavity) is discussed in light of similar issues arising in CQED (and in earlier work in magnetic resonance as well), as are certain problems relative to quantization of the electromagnetic near-field.
The idea behind this work is the supposition that it should be possible to introduce damping into the quantum mechanical discussion of a harmonic oscillator without a detailed description of the damping mechanism. A study is therefore made of an L, C circuit coupled to an artificial (or transmission) line, using a Hamiltonian formalism. The whole system is conservative but, for the transmission line case, the L, C circuit behaves as if it is damped. The most probable form for the Hamiltonian does not exhibit the damping in an obvious way. It is shown that by a suitable change of variables the Hamiltonian can be split into two time-dependent commuting parts, one of which has the form e -2α t ( P 2 /2 C ) + e 2α t ( Q 2 /2 L ) which has been previously used in a study of 2-level masers, and which does display the damping. The new operators Q and P are studied and it is shown that they are related to the charges and currents in the L, C circuit, but with the noise components due to the resistive loss (the transmission line) omitted. They are thus perhaps more natural variables to use than the actual charges and currents which do contain noise components. The problem of coupling a spin system to the current in the inductance is studied and the transition is made to the analogous problem of a spin system interacting with a damped mode of a cavity resonator. The analysis is compared with one given previously by Stevens and Josephson in 1959 and it is shown that the results previously obtained in a heuristic way are valid provided that noise fluctuations are negligible.
We numerically solve the Liouville equation for the Tavis Cummings model of multiple spins coupled to a lossless single mode cavity, starting from an initial condition with small numbers of fully polarized spins tipped by a specified angle, and the cavity in its ground Fock state. Time evolution of the magnetizations and cavity states, following small to medium nutation by a classical field, yields a microscopic quantum mechanical picture of radiation damping in magnetic resonance, and the formation of the free induction signal, that is, the transfer of Zeeman energy, via spin coherence, to cavity coherence. Although the motion of the Bloch vector is nonclassical, our quantum description is related to the macroscopic picture of NMR reception, by showing the close relationship between the usual radiation damping constant, and the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission.) That is, each is the product, of a nutation rate per oscillator current, and a current. Although the current in the damping constant is explicitly limited by cavity losses, which do not enter the formula for the Rabi frequency, we nonetheless show (in an appendix) how these losses can be introduced into our problem by means of a master equation. Numerical solution of the classical Bloch-Kirchhoff equations reinforces the conclusion that the strength of the free induction
We use a quasi-Hamiltonian formalism to describe the dissipative dynamics of a circuit-QED qubit that is affected by several fluctuating two-level systems with a 1/f-noise power spectrum. The qubit-resonator interactions are described by the Jaynes-Cummings model. We argue that the presence of pure dephasing noise in such a qubit-resonator system will also induce an energy relaxation mechanism via a fluctuating dipole-coupling term. This random modulation of the coupling is seen to lead to rich physical behavior. For non-Markovian noise, the coupling can either worsen or alleviate decoherence, depending on the initial conditions. The magnetization noise leads to behavior resembling the collapse and revival of Rabi oscillations if the photons are in a coherent state. For a broad distribution of noise couplings, the frequency of these oscillations depends on the mean noise strength. We describe this behavior semianalytically and find it to be independent of the number of fluctuators. This phenomenon could be used as an in situ probe of the noise characteristics.
When a two-state quantum system, capable of making radiative transitions, is driven by a high-frequency field, there occur damping effects due to the reaction of the sample to its own radiated field. This damping, which becomes important for high-Q rf structures and for samples of large dc susceptibilities, is here analyzed classically for a simple prototype system—a magnetic spin system obeying the Bloch equations. These equations are augmented to include the radiation-damping torques and are then solved for the four cases of usual interest. Firstly, for steady-state slow passage, radiation damping broadens and lowers the absorption and dispersion signals. Secondly, for adiabatic fast passage, damping causes the dispersion signal to dip at the line center and causes the otherwise absent absorption signal to become finite. However, if the radiation damping field becomes larger than the rf driving field a complete adiabatic inversion is shown to be no longer possible. Thirdly, the conditions for the occurrence of delayed power peaks of the free-precession signal are discussed. Fourthly, for the case of the driven nonsteady state, the stimulated emission may, for large radiation damping, become quite large if the system is driven from an initially ``negative temperature'' condition.
We show that there is excellent quantitative agreement between the usual semiclassical predictions for nuclear magnetic resonance experiments (quantized spins interacting with a classical radio frequency magnetic field, including radiation damping), and the predictions of a fully quantized description of the same experiment. We also propose a pictorial description of the relevant dynamical quantum states, which helps to lead the intuition towards the same conclusion. Our model ignores spin relaxation, and simulates the equivalent damping resistor of the sample circuit by a very long piece of lossless coaxial cable. The classical rf field (pulses and free induction decay) is described quantum mechanically by means of Glauber’s “coherent” or “quasiclassical” states.