The possibility of obtaining the initial pure state in a usual Stern-Gerlach experiment through the recombination of the two emerging beams is investigated. We have extended the previous work of Englert, Schwinger and Scully \cite{ISG1} including the fluctuations of the magnetic field generated by a properly chosen magnet. As a result we obtained an attenuation factor to the possible revival of coherence when the beams are perfectly recombined . When the source of the magnetic field is a SQUID(superconducting quantum interference device) the attenuation factor can be controlled by external circuits and the spin decoherence directly measured. For the proposed SQUID with dimensions in the scale of microns the attenuation factor has been shown unimportant when compared with the interaction time of the spin with the magnet.
The possibility of obtaining the initial pure state in a usual Stern-Gerlach experiment through the recombination of the two emerging beams is investigated. We have extended the previous work of Englert, Schwinger and Scully \cite{ISG1} including the fluctuations of the magnetic field generated by a properly chosen magnet. As a result we obtained an attenuation factor to the possible revival of coherence when the beams are perfectly recombined . When the source of the magnetic field is a SQUID(superconducting quantum interference device) the attenuation factor can be controlled by external circuits and the spin decoherence directly measured. For the proposed SQUID with dimensions in the scale of microns the attenuation factor has been shown unimportant when compared with the interaction time of the spin with the magnet.
The possibility of obtaining the initial pure state in a usual Stern-Gerlach experiment through the recombination of the two emerging beams is investigated. We have extended the previous work of Englert, Schwinger, and Scully [Found Phys. 18, 1045 (1988)] including the fluctuations of the magnetic field generated by a properly chosen magnet. As a result we obtained an attenuation factor to the possible revival of coherence when the beams are perfectly recombined. When the source of the magnetic field is a superconducting quantum interference device (SQUID) the attenuation factor can be controlled by external circuits and the spin decoherence directly measured. For the proposed SQUID with dimensions in the scale of microns the attenuation factor has been shown unimportant when compared with the interaction time of the spin with the magnet.
The Stern-Gerlach experiment (SGE) has been known for decades, but a complete theory that explains all facets of it remains enigmatic. In its classic realization, each spin state of an atom follows a unique path or trajectory in an SGE. The enigmatic part is the final output of SGE. Feynman envisaged the outcome to be an entangled state, a superposition of $|\text{spin}\phantom{\rule{4.pt}{0ex}}\text{state}\ensuremath{\rangle}\ensuremath{\bigotimes}|\text{corresponding}\phantom{\rule{4.pt}{0ex}}\text{path}\ensuremath{\rangle}$. Later works described the final state of SGE as a mixed state, a weighted average of states belonging to separate beams or trajectories. Notably, Schwinger, Englert, and Scully compared the difficulty of obtaining a coherent output (a pure state) to ``putting together Humpty Dumpty'' again. Yet recent experiments using Bose-Einstein condensates indicate the emerging beams are partly coherent, favoring Feynman's description. In this work, we revisit SGE using a recent version of the quantum master equation. We show that both outcomes are probable depending on the time of flight and the timescale of the environmental fluctuations. We predict the output is initially coherent and grows gradually into a mixed state. Moreover, we also estimate how the magnetic-field gradient helps broaden the beam waist. Moreover, our treatment implies that the wave function of an atom passing through a Stern-Gerlach device does not undergo an instantaneous collapse; rather, a gradual decay of coherences results in a mixed state, resulting in an irreversible process.
Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.
The Stern-Gerlach experiment is a seminal experiment in quantum physics, involving the interaction between a particle with spin and an applied magnetic field gradient. A recent article [Wennerström et al., Phys. Chem. Chem. Phys., 2012, 14, 1677-1684] claimed that a full understanding of the Stern-Gerlach experiment can only be attained if transverse spin relaxation is taken into account, generated by fluctuating magnetic fields originating in the magnetic materials which generate the field gradient. This interpretation is contrary to the standard quantum description of the Stern-Gerlach experiment, which requires no dissipative effects. We present simulations of conventional quantum dynamics in the Stern-Gerlach experiment, using extended Wigner functions to describe the propagation of the quantum state in space and time. No relaxation effects are required to reproduce the qualitative experimental behaviour. We also present simulations of quantum dynamics in the Rabi experiment, in which an applied radiofrequency field induces spin transitions in the particle wave.
We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the device. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in the presence of decoherence that shows a diffusive behavior for large values of the decoherence parameter. These features limit the dynamics of the present model. We also observe the decay of the nondiagonal terms with time and use this fact to quantify the amount of decoherence from the norm of those terms in phase space. From here, we can define a decoherence time scale, which differs from previous results that make use of the same model. We analyze a typical experiment and show that, for that setup, the decoherence time is much smaller than the characteristic time scale for the separation of the two beams, implying that they can be described as an incoherent mixture of atoms traveling in the up and down directions with opposite values of the spin projection. Therefore, entanglement is quickly destroyed in the setup we analyzed.
The Stern-Gerlach experiment consists of a beam composed by neutral spin 1/2 particles
that enters on a non-uniform magnetic field, which splits the beam into two, one of which consists of spin +1/2 particles and the other one consists of spin -1/2 particles. We initially consider that the particles are independent and do not interact. The objective of this work is to study and compare two cases. The first one is the case in which the particle with spin and spatial degrees of freedom initially independents is subjected to two consecutive Stern-Gerlach. The second one is similar to the first,
differing only by it's initial state, which is an entangled state of spin with a second spin 1/2 particle.