Stern-Gerlach Device Research Articles

Zig-zag dynamics in a Stern–Gerlach spin measurement

The century-old Stern–Gerlach setup is paradigmatic for a quantum measurement. We visualize the electron trajectories following the Bohmian zig-zag dynamics. This dynamics was developed in order to deal with the fundamentally massless nature of particles (with mass emerging from the Brout–Englert–Higgs mechanism). The corresponding trajectories exhibit a stochastic zig-zagging, as the result of the coupling between left- and right-handed chiral Weyl states. This zig-zagging persists in the non-relativistic limit, which will be considered here, and which is described by the Pauli equation for a non-uniform external magnetic field. Our results clarify the different meanings of ‘spin’ as a property of the wave function and as a random variable in the Stern–Gerlach setup, and they illustrate the notion of effective collapse. We also examine the case of an EPR-pair. By letting one of the entangled particles pass through a Stern–Gerlach device, the non-local influence (action-at-a-distance) on the other particle is manifest in its trajectory, e.g. by initiating its zig-zagging.

Lead position and lead-ring coupling effects on the spin-dependent transport properties in a two-dimensional network of quantum nanorings in the presence of Rashba spin–orbit interaction

The effects of lead positions and lead-ring coupling regimes are investigated for spin-related transport through a two-dimensional network of quantum nanorings (2DNQRs) considering Rashba spin–orbit interaction (RSOI) and magnetic flux. A matrix representation of the transmission and reflection coefficients through a single ring connected to the arbitrary number of leads has been introduced. As a specific example of 2DNQRs, the conductance, spin polarization and system efficiency are obtained via a triangular network of quantum rings (TNQRs). TNQRs are completely opaque or transparent versus RSOI strength and wave vector (k) of the incident electron. The periodicity of these functions along the k axis depends on the lead positions and is independent of lead-ring coupling. Also, the symmetric geometry and strong lead-ring coupling regime significantly improve the performance of the system as a multipurpose spintronic device (i.e., a perfect spin filter, spin splitter, spin switching, Stern–Gerlach device and an electronic switching device).

Nonlinear semi-classical 3D quantum spin

In an effort to provide an alternative method to represent a quantum spin, a precise 3D nonlinear dynamics method is used. A two-sided torque function is created to mimic the unique behavior of the quantum spin. A full 3D representation of the magnetic field of a Stern–Gerlach device was used as in the original experiment. Furthermore, the temporarily driven nonlinear damped model exhibits chaos, but struggles to be consistent through azimuthal angles in reproducing the well known quantum spin statistics.

Disentanglement of a Singlet Spin State in a Coincidence Stern-Gerlach Device

We analyze the spin coincidence experiment considered by Bell in the derivation of Bells theorem. We solve the equation of motion for the spin system with a spin Hamiltonian, Hz, where the magnetic field is only in the z-direction. For the specific case of the coincidence experiment where the two magnets have the same orientation the Hamiltonian Hz commutes with the total spin Iz, which thus emerges as a constant of the motion. Bells argument is then that an observation of spin up at one magnet A necessarily implies spin down at the other B. For an isolated spin system A-B with classical translational degrees of freedom and an initial spin singlet state there is no force on the spin particles A and B. The spins are fully entangled but none of the spin particles A or B are deflected by the Stern-Gerlach magnets. This result is not compatible with Bells assumption that spin 1/2 particles are deected in a Stern-Gerlach device. Assuming a more realistic Hamiltonian Hz + Hx including a gradient in x direction the total Iz is not conserved and fully entanglement is not expected in this case. The conclusion is that Bells theorem is not applicable to spin coincidence measurement originally discussed by Bell.

Shortcut to adiabaticity in a Stern-Gerlach apparatus

We show that the performances of a Stern-Gerlach apparatus can be improved by using a magnetic field profile for the atomic spin evolution designed through shortcut to adiabaticity technique. Interestingly, it can be made more compact - for atomic beams propagating at a given velocity - and more resilient to a dispersion in velocity, in comparison with the results obtained with a standard uniform rotation of the magnetic field. Our results are obtained using a reverse engineering approach based on Lewis-Riesenfeld invariants. We discuss quantitatively the advantages offered by our configuration in terms of the resources involved and show that it drastically enhances the fidelity of the quantum state transfer achieved by the Stern-Gerlach device.

Localized qubits in curved spacetimes

We provide a systematic and self-contained exposition of the subject of localized qubits in curved spacetimes. This research was motivated by a simple experimental question: if we move a spatially localized qubit, initially in a state |ψ1〉, along some spacetime path Γ from a spacetime point x1 to another point x2, what will the final quantum state |ψ2〉 be at point x2? This paper addresses this question for two physical realizations of the qubit: spin of a massive fermion and polarization of a photon. Our starting point is the Dirac and Maxwell equations that describe respectively the one-particle states of localized massive fermions and photons. In the WKB limit we show how one can isolate a two-dimensional quantum state which evolves unitarily along Γ. The quantum states for these two realizations are represented by a left-handed 2-spinor in the case of massive fermions and a four-component complex polarization vector in the case of photons. In addition we show how to obtain from this WKB approach a fully general relativistic description of gravitationally induced phases. We use this formalism to describe the gravitational shift in the Colella–Overhauser–Werner 1975 experiment. In the non-relativistic weak field limit our result reduces to the standard formula in the original paper. We provide a concrete physical model for a Stern–Gerlach measurement of spin and obtain a unique spin operator which can be determined given the orientation and velocity of the Stern–Gerlach device and velocity of the massive fermion. Finally, we consider multipartite states and generalize the formalism to incorporate basic elements from quantum information theory such as quantum entanglement, quantum teleportation, and identical particles. The resulting formalism provides a basis for exploring precision quantum measurements of the gravitational field using techniques from quantum information theory.

Conversion of heat to light using Townes’ maser-laser engine: Quantum optics and thermodynamic analysis

It is shown that thermal energy from a heat source can be converted to useful work in the form of maser-laser light by using a combination of a Stern-Gerlach device and stimulated emissions of excited particles in a maser-laser cavity. We analyze the populations of atoms or quantum dots exiting the cavity, the photon statistics, and the internal entropy as a function of atomic transit time, using the quantum theory of masers and lasers. The power of the laser light is estimated to be sufficiently high for device applications. The thermodynamics of the heat converter is analyzed as a heat engine operating between two reservoirs of different temperature but is generalized to include the change of internal quantum states. The von Neumann entropies for the internal degree are obtained. The sum of the internal and external entropies increases after each cycle and the second law is not violated, even if the photon entropy due to finite photon number distribution is not included. An expression for efficiency relating to the Carnot efficiency is obtained. We resolve the subtle paradox on the reduction of the internal entropy with regards to the path separation after the Stern-Gerlach device.

Stability of spintronic devices based on quantum ring networks

Transport properties in mesoscopic networks are investigated, where the strength of the (Rashba-type) spin-orbit coupling is assumed to be tuned with external gate voltages. We analyze in detail to what extent the ideal behavior and functionality of some promising network-based devices are modified by random (spin-dependent) scattering events and by thermal fluctuations. It is found that although the functionality of these devices is obviously based on the quantum coherence of the transmitted electrons, there is a certain stability: moderate level of errors can be tolerated. For mesoscopic networks made of typical semiconductor materials, even cryogenic temperatures can smear out the desired transport properties. When the energy distribution of the input carriers is narrow enough, it turns out that the devices can operate close to their ideal limits even at relative high temperature. As an example, we present results for two different networks: one that realizes a Stern-Gerlach device and another that simulates a spin quantum walker. Finally we propose a simple network that can act as a narrow band energy filter even in the presence of random scatterers.

Networks of Quantum Nanorings: Programmable Spintronic Devices

An array of quantum rings with local (ring by ring) modulation of the spin orbit interaction (SOI) can lead to novel effects in spin state transformation of electrons. It is shown that already small (3 x 3, 5 x 5) networks are remarkably versatile from this point of view: Working in a given network geometry, the input current can be directed to any of the output ports, simply by changing the SOI strengths by external gate voltages. Additionally, the same network with different SOI strengths can be completely analogous to the Stern-Gerlach device, exhibiting spatial-spin entanglement.

Proof of principle of SAPIS, a new type of polarized-ion source

A new type of polarized negative-ion source, based on the combination of an intense neutral Cs beam colliding with the polarized atomic H or D beam from a Stern–Gerlach device, and using a storage cell (SC) as ionization region, has been developed and tested. H- and D- ions were extracted from the SC. Their polarization was not yet measured. Extrapolation from this prototype source using results from most modern tested components such as the H/D atomic–beam and the Cs0 source shows an appreciable potential of this type of source with intensities comparable to or exceeding those of existing sources.

RefloGrad/GradTOF: Neutron energy analysis for a very high-flux neutron reflectometer

The possibility of analyzing the neutron energy coupled with a position-sensitive detector enables to perform specular reflectivity measurements on continuous neutron sources without any monochromator or chopper and thus permits intensity gains up to 20 compared to conventional reflectometers equipped with a monochromator or a chopper. In this communication, we present a spectrometer design using an energy analysis performed with a permanent magnet Stern–Gerlach device. We also propose a modified version of the spectrometer in which we combine the above setup with a high-speed chopper in order to perform classical TOF measurements (at a high repetition rate, up to 200 Hz) while still being able to use up to 30% of the full white spectrum available in the neutron guide.

Spintronic devices as quantum networks

We explore spintronics from a quantum information (QI) perspective. We show that QI specific methods can be an effective tool in designing new devices. Using the formalism of quantum gates acting on spin and mode degrees of freedom, we provide a solution to a reverse engineering problem, namely, how to design a device performing a given transformation between input and output. Among these, we describe an orientable Stern-Gerlach device and a new scheme to entangle two spins by transferring the entanglement from orbital to spin degrees of freedom. Finally, we propose a simple scheme to produce hyperentangled electrons, i.e., particles entangled in both the spin and mode degrees of freedom.

Spin State Determination Using a Stern-Gerlach Device

The well-known Stern-Gerlach device is proposed here for determination of a particle spin state instead of using it for measurement of spin observables. It is shown that measurement of particle momentum distributions (before and after the action of the device magnetic field) allows one to determine the particle initial spin state in the case of an arbitrary spin value. It is demonstrated that one cannot use for this purpose the usual treatment of the Stern-Gerlach experiment based on the entanglement of spin and spatial states.

Single and joint spin measurements with a Stern-Gerlach device

The measurement of spin-1/2 observables using a Stern-Gerlach type device is studied. A magnetic field with a dominant dipole component leads to a measurement of spin in one direction. The measurement is shown to be feasible (in principle) for electrons as well as for neutral particles. A quadrupole field leads to a joint measurement of two incompatible spin observables. Again, both the electron and the neutral case are presented. The accuracy of the joint measurement is compared to the limit imposed by the uncertainty principle.

Proposal for a Source of Polarized Protons

In a cyclotron, protons are produced by ionizing hydrogen atoms in the center of the magnet. If these atoms arrive in the ionizing region in states where the component of the proton spin along the field (I/sub 2/) has one value only, say +1/2, completely polarized protons could be available for acceleration. The variation of the four energy levels of a hydrogen atom, a(M/sub I= 1/2) and b(M/sub I =-1/2) E positive and c(M/sub I =-1/2/) and d(M/sub I/ = 1/2) E negative, as a function of the applied field is shown. It is relatively easy to separate, in an incoming beam of unpolarized hydrogen atoms, with a Stern-Gerlach device, those in states a and b from those in states c and d because of the large difference in magnetic moment. In the present proposal, once a beam of atoms distributed with equal populations between the states a and b has been obtained by a Stern-Gerlach device, all atoms in the b state are transferred into the d state by means of a radiofrequency field H/sub 1/ cos omega t parallel to the field H /sub 0/, by the adiabatic passage method. All proton spins are then in the statemore » I/sub 2/ = +1/2. (W.D.M.)« less