PDF Publication Title:
Text from PDF Page: 002
FANG ZHAO, FU-QUAN DOU, AND QING ZHAO PHYSICAL REVIEW RESEARCH 4, 013172 (2022) (a) ωa ωc (b) N=4 N=5 J(1+δ) δ<0 J(1-δ) δ >0 FIG. 1. (a) A schematic diagram of the SSH QB charging proto- col. It includes an N spin with a frequency of ωa. The spin chain has a nearest-neighbor hopping interaction with a strength of J. The δ is the dimerization parameter. The spin chain is coupled with a photon cavity with a frequency of ωc. (b) A schematic diagram of the SSH model spin chain with dimerization parameters δ < 0 and δ > 0 for spin numbers N = 5 and N = 6, respectively. QB with and without dimerization parameters in Secs. III and IV, respectively. The conclusion is given in Sec. V. II. MODEL In this paper, we study the energy charging and release of a SSH QB. Figure 1(a) shows the charging protocol. The phys- ical model of a SSH QB is an N-spin chain with frequency ωa. There is a hopping interaction between nearest-neighbor spins with strength J and the dimerization constant is δ. The QB is coupled with a cavity field with a cavity frequency of ωc. This cavity field transfers energy to charge the QB. Figure 1(b) shows the spin chain distribution for odd- and even-spin chains with different dimerization situations. The whole Hamiltonian of this SSH QB charging system is HS = HA + HB + HI . HA = ωcc†c, We consider the charging process of a SSH QB in a closed quantum system. Here, the initial state of the QB is the empty state |V0⟩ = |g⟩B, (2) where |g⟩ is the ground state of the QB. The charging of the QB is to let the empty QB gain energy from the external cavity. In our charging protocol, the cavity is full of energy. When the cavity and QB interaction strength g are nonzero, the QB will start charging. The dynamic charging process of the QB will be |ψ(t)⟩ = U|ψ(0)⟩ = e−iHSt|ψ(0)⟩. (3) |ψ(0)⟩ is the initial state of the whole system, |ψ(0)⟩ = |V0⟩ ⊗ |φ⟩. (4) |φ⟩ is the cavity state with full energy. We take the cavity initially in the Fock state, |φ⟩ = |nc⟩. (5) nc is the cavity photon number. Energy storage during the QB at time t is given by EB(t) = tr[HBρB(t)], where ρB (t ) = trA [ρS (t )] is the reduced density matrix of the QB at time t. The energy charged into the QB is equal to EB (t ) − EB (0), where EB (0) = EG is the ground state energy of the QB. Therefore, the actual charging energy of the QB is equal to E(t) = EB(t) − EG. (6) The E(t) is used to determine the energy charged into the QB. However, QB’s energy E(t) cannot be entirely released. According to the second law of thermodynamics, E (t ) cannot be wholly transformed into valuable work with- out dissipating heat. Therefore, the concept of ergotropy is introduced to characterize the ability to generate valuable work of a QB. The ergotropy is defined as εB (t ) = EB (t ) − min tr[HBU ρB (t )U † ]. (7) U N Ba+− H =ω −J(1+δ) −J(1−δ) i=1 ρB(t) = HB = rn(t)|rn(t)⟩⟨rn(t)|, en|en⟩⟨en|. σ(i)σ(i) N−1 The HB and ρB can be diagonalized and represented as i=2,4,6,... g(σ(i)c+H.c.). (i) (i+1) (σ+ σ− (i) (i+1) (σ+ σ− +H.c.) +H.c.), n n i=1,3,5,... N−2 The eigenvalues of ρ (t) are arranged in descending order B as r0 r1 ···, and the eigenvalues of HB are arranged in ascending order as e0 e1 ···. The second term on the right-hand side of the definition of ergotropy can be simplified as rnen. (8) III. CHARGING PROPERTIES WITHOUT DIMERIZATION PARAMETER In this section, we investigate the charging process of a QB without considering the dimerization parameter. Then we N I+ i=1 ing system. HA is the cavity Hamiltonian. ωc is the cavity field frequency. HB is the SSH QB Hamiltonian. J is the nearest-neighbor hopping strength between spins. δ is the dimerization parameter. HI is the interaction term between the cavity and the QB. g is the coupling constant between the spin and the cavity. H = Here, HS is the total Hamiltonian of the whole QB charg- (1) 013172-2 mintr[HUρ(t)U†] = U nPDF Image | Charging performance of the Su-Schrieffer-Heeger quantum battery
PDF Search Title:
Charging performance of the Su-Schrieffer-Heeger quantum batteryOriginal File Name Searched:
2105-00258.pdfDIY PDF Search: Google It | Yahoo | Bing
Sulfur Deposition on Carbon Nanofibers using Supercritical CO2 Sulfur Deposition on Carbon Nanofibers using Supercritical CO2. Gamma sulfur also known as mother of pearl sulfur and nacreous sulfur... More Info
CO2 Organic Rankine Cycle Experimenter Platform The supercritical CO2 phase change system is both a heat pump and organic rankine cycle which can be used for those purposes and as a supercritical extractor for advanced subcritical and supercritical extraction technology. Uses include producing nanoparticles, precious metal CO2 extraction, lithium battery recycling, and other applications... More Info
| CONTACT TEL: 608-238-6001 Email: greg@infinityturbine.com | RSS | AMP |