T ( a0 , 0 ) + 2 = n. Within this case, the state is left unchanged by the rotation (note that squeezed states have a -rotational symmetry) such that it really is squeezed inside the identical path every single time. This squeezing will not turn out to be infinite; on the other hand, because the dynamics also involves a relaxation rate. Thus, we anticipate a spike inside the squeezing in the final state when = n/2 – rot ( a0 , 0 )/2. Finally, we note that we have purpose to think that rot ( a0 , 0 ) is small for all a0 and 0 . Recall that rot ( a0 , 0 ) may be the amount of rotation offered by the interaction image map I . The interaction image is developed to eliminate the no cost evolution/rotation in the 1,2 program. Therefore, rot ( a0 , 0 ) only corresponds to the rotation induced in the probe by the interaction Hamiltonian. Thus, we expect spikes in the squeezing at n/2 which can be just what we see. Appendix D. Facts on Mode Convergence As we discussed inside the major text, we truncate the amount of cavity modes viewed as to make our computations tractable. In this section, we study the convergence of our results with the quantity of cavity modes thought of. We count on our scenario to have better convergence behavior than other prior studies on probes accelerating inside optical cavities (such as e.g., [28]) given that in our setup the probe does not attain ultrarelativistic speeds with respect to the cavity walls. As such, the probe’s gap P will not sweep across quite a few cavity modes as it is blue/redshifted ( P max P ) with respect towards the lab frame. As an example, with 0 = /16 and a0 = 10 we’ve max = 1 + a0 such that max 0 = 11/16. Please note that even whenSymmetry 2021, 13,18 ofmaximally blue-shifted, the probe Penicolinate A Technical Information frequency is still beneath the frequency of the very first cavity mode 0 = . Another reason that one could worry that a lot of cavity modes are needed for convergence is that the probe all of a sudden couples/decouples from each and every cavity. Certainly, one can Linoleoyl glycine References believe in the probe possessing a top-hat switching function, . Normally, one would expect that such a sudden adjust within the coupling would make high frequency cavity modes relevant. Nonetheless, a essential design and style function of our setup regulates the suddenness of this switching. Particularly, the cavity’s Dirichlet boundary conditions enforce that the probe is successfully decoupled from the field at the time of this switching. Taken together, these suggest that not too a lot of cavity modes will be needed for convergence. Let us see how these expectations play out when we truly put them to the test. Figure A5 shows the 0 = /16 line of Figure 1b of the major text converging as we increase the amount of field modes, N, which we look at. Unsurprisingly, as the acceleration increases, we require far more cavity modes for convergence. Figure A5 suggests that making use of N = 20 modes is sufficient when a0 6 and that employing N = 200 is sufficient when a0 100.1.0 0.8 0.6 0.four 0.two -1.0 -0.five 0.dT0 /daN=10 N=20 N=30 N=60 N=Log10 (a0 ) 0.five 1.0 1.five two.N=160 N=Figure A5. Derivative of your probe’s final dimensionless temperature T0 = k B TL/c with respect h to the acceleration a0 = aL/c2 as a function of a0 on log-scale. The dimensionless probe gap, 0 = P L/c = /16, as well as the dimensionless coupling strength, 0 = L/ hc = 0.01, are fixed. The black-dashed line is at dT0 /da0 = 1/2. The colored lines show the values of dT0 /da0 which result from contemplating only N cavity modes where N = ten, 20, 30, 60, 110, 160, and 210. These lines split off from the rest one particular at a time in order from left to appropriate.
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