Test of the linearity of quantum mechanics in optically pumpedHg201

Abstract

Measurement of the free precession of nuclear spins in optically pumped ground-state 30l Hg atoms has allowed a test of Weinberg's nonlinear generalization of quantum mechanics. Shifts among the three resolved precession frequencies in the spin-\ system were studied as a function of the projection of spin polarization along the precession axis. Our results set an upper limit on <f, Weinberg's nonlinearity parameter, of \e\l2nh < 3.8 //Hz, which corresponds to 2.0 x 10 -27 of the binding energy per nucleon. This is the most stringent such limit to date.PACS numbers: 03.65. Bz, 06.30.Ft, 32.80.Bx, 76.60.Es Recently, Weinberg has formulated a nonlinear version of the Schrodinger equation that in lowest order reduces to ordinary quantum mechanics. 12 Several groups have since reported upper limits 3 " 5 on the nonlinearity parameter e introduced by Weinberg. These results underscore the importance of precise measurements to verify the accuracy of the Schrodinger equation independently of any specific quantum-mechanical system. We report here the results of an experimental study of the spin-precession frequencies of optically pumped 201 Hg. The limit on possible nonlinear quantummechanical (NLQM) effects set by our measurement is the most stringent to date and results from a novel analysis technique.In addition to the "ordinary" quantum-mechanical Hamiltonian, Weinberg's generalized theory contains terms proportional to powers of y/* y/ making the overall energy dependent on the wave-function amplitude. Our discussion is limited to the discrete system described by the four ground-state Zeeman levels of 20l Hg (/ = F= y) in a magnetic field. In this case, the lowestorder nonlinear Schrodinger equation takes the formwhere Ti^ is the zeroth-order energy of Zeeman level ju, N is the norm of the wave function, S^v is a constant tensor, and p.,v G {4 ,1,-f ,-f}. Possible terms of the form (ii/fSitvv'Vv^Vv for v^v time average to zero in our case (i.e., when the three Zeeman frequencies are resolved, as described below).We search for the effect of nonlinearities by measuring the precession frequency of the 201 Hg nuclear spins as a function of y/*y/, in our case as a function of the cone angle of precession. We use optical pumping to polarize the spins at various angles 0 relative to the final precession axis, and measure the frequency of free precession by the modulation it produces in the transmission of the pumping light. To apply Eq. (l) to our experiment we begin by rewriting the wave-function probabilities y/*y/ v /N as diagonal elements of the density matrix p^\ The superscript indicates that the elements are defined along the initial polarization direction (pump axis). It is then convenient to re-express the individual p[^ in a basis of orthogonal spherical tensors, T L( h and corresponding multipole polarizations, defined by pi°o = Tr(p (0) T L o). 6J In the spin-y case, the ensemble is characterized by dipole, quadrupole, and octupole polarizations. The nonlinear corrections to the energies now have the form v...

Some Trends in Quantum Thermodynamics

“…New experimental evidence (e.g., [1][2][3][4][5][6][7][8][9][10]) over the last three decades has seen the emergence at atomistic scales of the phenomenon of "spontaneous decoherence", which in turn has led to a revival of interest in matters related to the unitary foundations of quantum mechanics (QM) and what if anything the 2nd Law of thermodynamics may have to say about this. Thus, despite the fact that some call it a "tired old mystery" [11], the search for the origin and the true nature of the 2nd Law has recently gained new traction.…”

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Nonlinear Dirac Equations

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Dynamic effects in nonlinear magneto-optics of atoms and molecules: review

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