Studying Heisenberg-like Uncertainty Relation with Weak Values in One-dimensional Harmonic Oscillator

As one of the fundamental traits governing the operation of quantum world, the uncertainty relation, from the perspective of Heisenberg, rules the minimum deviation of two incompatible observations for arbitrary quantum states. Notwithstanding, the original measurements appeared in Heisenberg’s principle are strong such that they may disturb the quantum system itself. Hence an intriguing question is raised: What will happen if the mean values are replaced by weak values in Heisenberg’s uncertainty relation? In this work, we investigate the question in the case of measuring position and momentum in a simple harmonic oscillator via designating one of the eigenkets thereof to the pre-selected state. Astonishingly, the original Heisenberg limit is broken for some post-selected states, designed as a superposition of the pre-selected state and another eigenkets of harmonic oscillator. Moreover, if two distinct coherent states reside in the pre- and post-selected states respectively, the variance reaches the lower bound in common uncertainty principle all the while, which is in accord with the circumstance in Heisenberg’s primitive framework.

Uncertainty Relations in the Madelung Picture

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

Nonclassicality of photon-modulated spin coherent states in the Holstein-Primakoff realization

Two new photon-modulated spin coherent states (SCSs) are introduced by operating the spin ladder operators J ± on the ordinary SCS in the Holstein-Primakoff realization and the nonclassicality is exhibited via their photon number distribution, second-order correlation function, photocount distribution and negativity of Wigner distribution. Analytical results show that the photocount distribution is a Bernoulli distribution and the Wigner functions are only associated with two-variable Hermite polynomials. Compared with the ordinary SCS, the photon-modulated SCSs exhibit more stronger nonclassicality in certain regions of the photon modulated number k and spin number j, which means that the nonclassicality can be enhanced by selecting suitable parameters.

Coherent states for a system of an electron moving in a plane: case of discrete spectrum

In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and continuous spectra. The eigenfunctions are realized as an orthonormal basis of a suitable Hilbert space appropriate for building the related coherent states. These latter are achieved in the context where we consider both spectra purely discrete obeying the criteria that a family of coherent states must satisfies.

Relative Entropy of Coherent States on General CCR Algebras

For a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitationthereof. We give a unified formula for this entropy in terms of single-particle modular data. Further, we investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces; here convexity of the entropy (as usually considered for the Quantum Null Energy Condition) is replaced with lower estimates for the second derivative, composed of “bulk terms” and “boundary terms”. Our main assumption is that the subspaces are in differential modular position, a regularity condition that generalizes the usual notion of half-sided modular inclusions. We illustrate our results in relevant examples, including thermal states for the conformal U(1)-current.

Quantum coherence induced by a flux qubit coupled by a resonator coherent field through a two-photon interaction

The intrinsic decoherence effects on a flux qubit coupled to a resonator through a two-photon interaction where the resonator field is initially in coherent and even coherent states are investigated. The qubit-resonator entanglement and coherence loss (mixedness) of the system and its subsystems are examined using entropy and negativity. The ability of the qubit-resonator interaction to generate quantum coherence (qubit-resonator entanglement and the mixedness) is shown to be dependent on the initial cavity non-classicality, detuning, and decoherence. For larger values of the qubit-resonator detuning, the initial resonator non-classicality can enhance the generation and stability of quantum coherence. The decoherence degrades the qubit-resonator entanglement and destroys the sudden death-birth entanglement.

Performance of microheaters for tunable on-chip interferometer

Mach-Zehnder interferometer (MZI) is a valuable practical tool in many optical science areas. In particular, high-contrast MZI are required for experimental realization of displacement-based quantum receivers that can discriminate weak coherent states of light with the minimum error rate. In this work we study phase modulators of tunable on-chip interferometer on silicon nitride (Si3N4) platform for telecom wavelength (1550 nm) consisting of several MZI. Phase modulators on one of the arms of MZI consists of microheaters and waveguide. Microheaters heat waveguides changing its refractive index due to thermo-optical effect providing a phase shift. We measure the bandwidth of phase modulators and study their operation in pulse mode.

Seesaw, coherence and neutrino oscillations

We present a prescription for consistently constructing non-Fock coherent flavour neutrino states within the framework of the seesaw mechanism, and establish that the physical vacuum of massive neutrinos is a condensate of Standard Model massless neutrino states. The coherent states, involving a finite number of massive states, are derived by constructing their creation operator. This construction fulfills automatically the key requirement of coherence for the oscillations of particles to occur. We comment on the inherent non-unitarity of the oscillation probability induced by the requirement of coherence.