Insensitivity of spin dynamics to the orbital angular momentum transferred from twisted light to extended semiconductors

We study the spin dynamics of carriers due to the Rashba interaction in semiconductor quantum disks and wells after excitation with light with orbital angular momentum. We find that although twisted light transfers orbital angular momentum to the excited carriers and the Rashba interaction conserves their total angular momentum, the resulting electronic spin dynamics is essentially the same for excitation with light with orbital angular momentum $l=+|l|$ and $l=-|l|$. The differences between cases with different values of $|l|$ are due to the excitation of states with slightly different energies and not to the different angular momenta per se, and vanish for samples with large radii where a $k$-space quasi-continuum limit can be established. These findings apply not only to the Rashba interaction but also to all other envelope-function approximation spin-orbit Hamiltonians like the Dresselhaus coupling.Comment: 5 pages, 2 figure

Understanding and utilizing the inner bonds of process tensors

Process tensor matrix product operators (PT-MPOs) enable numerically exact simulations for an unprecedentedly broad range of open quantum systems. By representing environment influences in MPO form, they can be efficiently compressed using established algorithms. The dimensions of inner bonds of the compressed PT-MPO may be viewed as an indicator of the complexity of the environment. Here, we show that the inner bonds themselves, not only their dimensions, have a concrete physical meaning: They represent the subspace of the full environment Liouville space which hosts environment excitations that may influence the subsequent open quantum systems dynamics the most. This connection can be expressed in terms of lossy linear transformations, whose pseudoinverses facilitate the extraction of environment observables. We demonstrate this by extracting the environment spin of a central spin problem, the current through a quantum system coupled to two leads, the number of photons emitted from quantum emitters into a structured environment, and the distribution of the total absorbed energy in a driven non-Markovian quantum system into system, environment, and interaction energy terms. Numerical tests further indicate that different PT-MPO algorithms compress environments to similar subspaces. Thus, the physical interpretation of inner bonds of PT-MPOs both provides a conceptional understanding and it enables new practical applications

Sublinear scaling in non-Markovian open quantum systems simulations

Funder: M.C. and E.M.G. acknowledge funding from EPSRC grant no. EP/T01377X/1. B.W.L. and J.K. were supported by EPSRC grant no. EP/T014032/1.While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps n. Here, we introduce a numerically exact algorithm to calculate process tensors—compact representations of environmental influences—which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent the environment. It is applicable to environments with Gaussian statistics, such as for spin-boson-type open quantum systems. Based on a divide-and-conquer strategy, our approach requires only (n log n) singular value decompositions for environments with infinite memory. Where the memory can be truncated after nc time steps, a nominal scaling (nc log nc) is found, which is independent of n. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach, we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The observed computation time is not necessarily proportional to the number of singular value decompositions because the matrix dimensions also depend on the number of time steps. Nevertheless, quasilinear and sublinear scaling of computation time is found in practice for a wide range of parameters. While there are instances where existing methods can achieve comparable nominal scaling by precalculating effective propagators for time-independent or periodic system Hamiltonians, process tensors contain all the information needed to extract arbitrary multitime correlation functions of the system when driven by arbitrary time-dependent system Hamiltonians. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but it also has fundamental implications for the simulation complexity of tensor network approaches.Publisher PDFPeer reviewe

Tree-like process tensor contraction for automated compression of environments

Funding: M.C. and E.M.G. acknowledge funding from EPSRC grant no. EP/T01377X/1. B.W.L. and J.K. acknowledge funding from EPSRC grant no. EP/T014032/1.The algorithm “automated compression of environments” (ACE) [M. Cygorek et al., Nat. Phys. 18, 662 (2022)] provides a versatile way of simulating an extremely broad class of open quantum systems. This is achieved by encapsulating the influence of the environment, which is determined by the interaction Hamiltonian(s) and initial states, into compact process tensor matrix product operator (PT-MPO) representations. The generality of the ACE method comes at high numerical cost. Here, we demonstrate that orders-of-magnitude improvement of ACE is possible by changing the order of PT-MPO contraction from a sequential to a treelike scheme. The problem of combining two partial PT-MPOs with large inner bonds is solved by a preselection approach. The drawbacks of the preselection approach are that the MPO compression is suboptimal and that it is more prone to error accumulation than sequential combination and compression. We therefore also identify strategies to mitigate these disadvantages by fine-tuning compression parameters. This results in a scheme that is similar in compression efficiency and accuracy to the original ACE algorithm, yet is significantly faster. Our numerical experiments reach similar conclusions for bosonic and fermionic test cases, suggesting that our findings are characteristic of the combination of PT-MPOs more generally.Peer reviewe

Sublinear scaling in non-Markovian open quantum systems simulations

While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps $n$. Here, we introduce a numerically exact algorithm to calculate process tensors -- compact representations of environmental influences -- which provides a scaling advantage over previous algorithms by leveraging self-similarity of the tensor networks that represent Gaussian environments. Based on a divide-and-conquer strategy, our approach requires only $\mathcal{O}(n\log n)$ singular value decompositions for environments with infinite memory. Where the memory can be truncated after $n_c$ time steps, a scaling $\mathcal{O}(n_c\log n_c)$ is found, which is independent of $n$. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dot-phonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but also has fundamental implications for simulation complexity

On-demand generation of higher-order Fock states in quantum-dot--cavity systems

The on-demand preparation of higher-order Fock states is of fundamental importance in quantum information sciences. We propose and compare different protocols to generate higher-order Fock states in solid state quantum-dot--cavity systems. The protocols make use of a series of laser pulses to excite the quantum dot exciton and off-resonant pulses to control the detuning between dot and cavity. Our theoretical studies include dot and cavity loss processes as well as the pure-dephasing type coupling to longitudinal acoustic phonons in a numerically complete fashion. By going beyond the two-level approximation for quantum dots, we study the impact of a finite exchange splitting, the impact of a higher energetic exciton state, and an excitation with linearly polarized laser pulses leading to detrimental occupations of the biexciton state. We predict that under realistic conditions, a protocol which keeps the cavity at resonance with the quantum dot until the desired target state is reached is able to deliver fidelities to the Fock state $| 5\rangle$ well above $40\,\%$.Comment: 12 pages, 8 figure