Band gaps induced by vacuum photons in closed semiconductor cavities

Abstract

We consider theoretically a closed (zero-dimensional) semiconductor microcavity where confined vacuum photonic mode is coupled to electrons in valence band of the semiconductor. It is shown that vacuum-induced virtual electron transitions between valence and conduction bands result in renormalization of electron energy spectrum. As a consequence, vacuum-induced band gaps appear within the valence band. Calculated values of the band gaps are of sub-meV scale, that makes this QED effect to be measurable in state-of-the-art experiments.PACS numbers: 42.50. Pq, 42.50.Hz, 71.20.Mq Introduction.-There are physical situations where the electron-photon interaction cannot be considered as a weak perturbation (so-called regime of strong lightmatter coupling). In this regime, it is necessary to consider the system "electron + field" as a whole. Such a bound electron-photon object, which was called "electron dressed by field" (dressed electron), became commonly used model in modern physics [1,2]. The interest in this field is stimulated by the possibility of the achievement of the hybrid -half-light half-matter -excitations which can demonstrate peculiar properties. Therefore, the regime of strong light-matter coupling was extensively investigated both theoretically and experimentally in a variety of the systems, including optical planar microcavities with semiconductor [3-5] and organic [6][7][8] quantum wells, microcavities with individual quantum dots [9-11] and others. Effects of strong coupling can be used for variety of technological applications [12], including novel types of the lasers [13,14], optical switches and logic gates [15][16][17], all-optical integrated circuits [18], sources of entangled photon pairs [19] and others. Among most bright phenomena of strong light-matter coupling, we have to note the field-induced modification of energy spectrum of dressed electrons -also known as a dynamic (ac) Stark effect -which was discovered in atoms many years ago [20] and has been studied in details in various atomic and molecular systems [1,2]. For solids, the dynamic Stark effect results in the gap opening within electron energy bands [21][22][23][24][25].In order to turn usual "bare" electrons into "dressed" electrons, a characteristic energy of electron-photon interaction should be increased. This can be done in two different ways. The first of them consists in using a strong laser-generated electromagnetic field (the case of large photon occupation numbers) [1,2]. The second way consists in decreasing the effective volume where electron-

Entanglement harvesting in double-layer graphene by vacuum fluctuations in a microcavity

“…( 18) numerically for ∆t = 0 and ∆k = 0 for different sets of values of d 1 /L and d 2 /L, the negativity estimator shows a critical value of ∆kL ∼ 3.2 where the negativity changes sign (see figure 6 ). By considering L = 500nm as a normal microcavity, the induced gap is ǫ G ∼ 6×10 −15 eV which is smaller than typical induced gaps in normal semiconductors [48]. Following the same procedure, we can consider that the initial quantum state for the two electrons in each graphene sheet is given by eigenstates of the Hamiltonian which can be written as a superposition of the sublattice basis.…”

Cavity‐photon contribution to the effective interaction of electrons in parallel quantum dots

“…When dealing with a system with two types of interactions, like the electron‐electron interaction, and the electron‐photon interaction, one typically may start by building a Green function for the electron including the mutual electron interaction. A second step would be to evaluate the Green function of the full system dressed by the photons . Similarly, in a CI‐approach, one starts by diagonalizing the Hamiltonian matrix for the Coulomb interacting electrons, constructs a new many‐body Fock‐basis from the states of the Coulomb interacting electrons and possibly the photon number operator, and diagonalizes then the full Hamiltonian matrix .…”

“…A second step would be to evaluate the Green function of the full system dressed by the photons. 17 Similarly, in a CI-approach, one starts by diagonalizing the Hamiltonian matrix for the Coulomb interacting electrons, constructs a new many-body Fockbasis from the states of the Coulomb interacting electrons and possibly the photon number operator, and diagonal-izes then the full Hamiltonian matrix. 18 This approach has been termed: "Stepwise introduction of model complexity".…”