![]() ![]() Pritchard, Optics and interferometry with atoms and molecules. This process is experimental and the keywords may be updated as the learning algorithm improves. These keywords were added by machine and not by the authors. ![]() Finally, the interference and tunneling of two condensates, confined in nearby potential wells, is considered, and the condensate analogue of Josephson oscillations is described. Based on recent theoretical models, we speculate on the possible observation of quantum gravitational fluctuations, by using matter wave interferometry. In the frame of the quantum theory of gravitation, still under construction, a fluctuating space-time foam should exist at the Planck space-time scale. We then consider decoherence of atom interference fringes, associated with quantum fluctuations of gravitational space-time. Atom interferometers are briefly discussed, and decoherence processes are introduced. Presumably, the reason it is often not distinguished from $T_2$ in papers is that it is assumed that such inhomogeneities always exist and so $T^*_2$ is almost always the value being measured and the most relevant in practise.In this chapter, we explore the topic of matter wave interferometry and of quantum coherence, which plays a central role in quantum theory and is also used for many experimental applications. So, if I am understanding this correctly (and I am not an expert in this), then $T_2^*$ is the combined dephasing from the standard dephasing mechanism (described by $T_2$) and any inhomogeneities in the DC field. A new time constant is often referred to as $T_2^*$. A time constant for this dephasing process is determined by the spatial (not temporal) inhomogeneous broadening of the DC field and distinguished from $T_2$ process. This leads to the dephasing effect if we compare the phase difference between different qubits. If many spin qubits are placed in such an inhomogeneous DC field, they have different Larmor frequencies. If you want to go check it out on a real experiment you can try the notebook but you need an account on the IBM Q experience.įrom Chapter 15 of NII's quantum information lecture series on "Fundamentals of Noise processes" (link here):Īn applied DC field $H_0$ is not completely uniform in all space points. I similar but different expression can be derived for the second experiment and I will leave as an exercise what happens but depending on the assumptions you are willing to make about the noise correlations you can simplify this expression in terms of the noise spectrum. Wait makes $(|0\rangle+\exp(-i\Delta t)|1\rangle)/\sqrt(0) = 1/2+\langle\cos(\int_0^t \Delta(t))\rangle/2$ where we have averaged over different shots (runs of the experiment). To see this imagine the simplest case where the noise can be explained by a Hamiltonian $H = \Delta |1\rangle\langle 1|$ that is constant and unknown. There are higher order experiments that refocus the noise better and this is an active research area. In the second experiment, the pi-pulse refocuses slow noise which depending on the system can be due to many reasons. The decay time of this experiment is $T_2$. We commonly call this a Ramsey experiment.Įxperiment two: Prepare the qubit in a superposition state and apply half the wait time and then apply a pi-pulse (X operator) and then the remainder of the wait time and measure in the superposition basis. ![]() The decay time of this experiment is $T_2^*$. The naming started in NMR and it has become the difference between the following two experiments.Įxperiment one: Prepare the qubit in a superposition state (apply a H gate) and vary the wait time and then measure in the superposition basis (apply another H gate). ![]()
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