Rydbergatomstudynote.md

Rydberg atoms in experiments

Rydbeg atoms are not the atoms corresponding to a particular element, but rather a class of excited state atoms with many electrons in the outer layers of the atoms. The Rydberg atoms are characterized by the fact that the outermost electron is in a state with a very high principal quantum number.

We can excited an atom to a high energy level, when the energy level is high enough, the principal quantum number is large enough, this atom will be excited to a Rydberg state, which is called Rydberg atom.

The Rydberg atoms have a number of interesting properties, such as a very large atomic radius and a very long lifetime. The Rydberg atoms are also very sensitive to external electric and magnetic fields, and are therefore used in a number of applications, such as quantum computing and quantum optics.

When n>>1, Rydberg atoms will have dipole-dipole interactions proportional to $n^4$, and radiative lifetimes proportional to $n^3$. The dipole-dipole interactions will influence the energy levels of atoms, make a move them. The ground state atoms round Rydberg atoms will lift their energy level, so that a laser beam that could have excited this ground state atom to the Rydberg state, now the laser can't reach the Rydber energy level. This is called the Rydberg blocking, and it is a very important property.

What is dipole? What is dipole-dipole interactions?

• A dipole is a physical term used to describe a molecule or atom in which there is a separation of positive and negative charges, resulting in a net dipole moment. This means that the molecule or atom has a slightly positive end and a slightly negative end.

• Dipole-dipole interactions refer to the attractive forces that occur between the positive end of one polar molecule and the negative end of another polar molecule. These interactions are one of the types of intermolecular forces, which are the forces of attraction or repulsion between molecules. Dipole-dipole interactions are relatively weak compared to covalent or ionic bonds, but they play an important role in determining the physical properties of substances, such as boiling and melting points, solubility, and viscosity.

When we research the Rydberg atoms, we usually use the laser to excite the atoms to the Rydberg state. We always choose the heavy atoms to excite, because the heavy atoms have a large principal quantum number, the energy level of the outer layer electrons is high enough, so the heavy atoms are easier to excite to the Rydberg state. Because the single electron of the outermost layer is easier to excite, so we prefer to choose the alkali metal atom. Now people often use Rb atom or Sr atom to reach the Rydberg state.

In Rydberg atoms, the size of electron cloud is proportional to $n^2$, so the size of Rydberg atoms is very large. This will influence other properties of Rydberg atoms in proportion to the power of n, such as the dipole-dipole interactions and the radiative lifetimes. For the same atom, which has a small ground state wave function when its outmost layer electrons are in the ground state. When it is excited to the Rydberg state, the wave function will be very large. So the spatial overlap between the ground state wave function and the Rydberg state wavefunction with high principal quantum number will be very small, so the coupling between the ground state and the Rydberg state will be very weak. This has two effects: one is that it is really hard to use lasers to excite the ground state atom to the Rydberg state because of the weak coupling, but this property also means the other effect: Rydberg state is difficult to decay to the ground state, the Rydberg atoms have a long lifetime.Experimentally such Rydberg atomic lifetimes are measurable, up to roughly on the order of a hundred microseconds, with ordinary low excited states having lifetimes of only a few tens of nanoseconds.

The complexity of regulating quantum states in pratical experiment is mainly limited by the lifetime of the quantum state. The longer the lifetime, the more complex the degree of the quantum state. So the long lifetime of the Rydberg state can allow us to do more operations to this system, and we can implement more regulation programmes in practical experiment.

A ground atom is hard to excite to the Rydberg state by one laser photon, because the energy difference between the ground state and the Rydberg state is very large. But we can use two laser photons to excite the ground state atom to the Rydberg state, this is called the two-photon excitation. The two-photon excitation is a very important method to excite the Rydberg atoms, and it is widely used in the experiment.

Rydberg atoms in quantum information

What is neutral atom qubits?

• Neutral atom qubits are a type of qubit, the fundamental unit of quantum information processing, that uses individual neutral atoms as the basis for storing and manipulating quantum information. These qubits are typically realized using laser-cooled and trapped neutral atoms, which can be precisely controlled and manipulated using techniques such as laser beams and magnetic fields.Neutral atom qubits have several advantages, including long coherence times, which means that the quantum information stored in the qubits can be preserved for relatively long periods of time. This makes them a promising candidate for building scalable and fault-tolerant quantum computing systems.

What is neutral atom?

• A neutral atom is an atom that has an equal number of protons and electrons, resulting in a net charge of zero. In other words, the positive charge of the protons in the nucleus is balanced by the negative charge of the electrons orbiting the nucleus. Atoms are the basic building blocks of matter, and they consist of a nucleus, which contains protons and neutrons, surrounded by a cloud of electrons. The number of protons in the nucleus determines the element to which the atom belongs, while the number of electrons determines the atom's overall charge. Neutral atoms are the most common state of atoms in nature, as they are stable and do not carry any net electrical charge. When an atom loses or gains electrons, it becomes an ion, which carries a net positive or negative charge, respectively.

What is qubit?

• A qubit is the fundamental unit of quantum information processing, analogous to the classical bit in classical computing. Unlike classical bits, which can be in one of two states (0 or 1), qubits can exist in a superposition of states, meaning that they can be in a combination of 0 and 1 at the same time. This property allows qubits to perform multiple calculations simultaneously, making them potentially much more powerful than classical bits for certain types of computations. Qubits are typically realized using quantum systems such as individual atoms, ions, or superconducting circuits, and they are the building blocks of quantum computers and other quantum information processing devices.

Rydberg atom was proposed a decade ago to take advantage of its properties to implement quantum gates between neutral atom qubits. The availabillity of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks streching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics.

Quantum simulation and computing with Rydberg-interacting qubits

Arrays of optically trapped atoms excited to Rydberg states have recently emerged as a competitive physical platform for quantum simulation and computing, where high-fidelity state preparation and readout, quantum logic gates, controlled quantum dynamics of more than 100 qubits have all been demonstrated.

overview of:

• high degree of flexibility for encoding qubits
• performing quantum operations
• engineering quantum many--body Hamiltonians

review of:

• high-fidelity state quantum operations
• logic gates
• quantum simulations in many-body regimes

future:

• computing schemes that are particularly suited to the Rydberg platform
• remaining challenges to quantum simulators and quantum computers

What is quantum simulation and computing?

• The basic idea is to prepare a set of quantum objects (atoms, ions, photons, etc.) in a well defined quantum state and to transform this state by making them interact in controlled ways.

• In this way we can overcome the intrinsic limitatons of classical devices when representing multi-particle quantum states and their evolution.

What is high-fidelity quantum logic operations and high-fidelity state quantum operations?

• High-fidelity quantum logic operations refer to the ability to perform quantum operations with a high degree of accuracy and precision. This means that the operations are executed in such a way that the quantum state of the system is preserved as much as possible, minimizing errors and maintaining the integrity of the quantum information.

• High-fidelity state quantum operations, on the other hand, specifically refer to the ability to prepare and manipulate quantum states with high precision and accuracy. This includes operations such as creating, controlling, and measuring quantum states with minimal error or distortion, allowing for reliable and accurate quantum information processing.

An analog quantum simulator is a physical system which mimics another quantum system of interest, or a specific class of models, by reproducing its Hamiltonian as close as possible. By performing controlled experiments and measurements on the quantum simulator we can then learn something about the target system which is hard by using classical computers.

A digital quantum simulator performs a similar task by encoding the quantum state of the target system in a quantum register.

If quantum gates constitute a universal set then in principle a digital quantum simulator can simulate any local Hamiltonian, including those with terms that are not natively realized by the physical system.

A quantum computer takes this a step further, making use of a set of fully addressable qubits and universal set of quantum logic gates (possibly including error correction) to implement quantum algorithms for efficiently solving classically intractable computational problems.

Another very promising approach to quantum information processing based on trapped neutral atoms.

The basic idea is to encode quantum information in the internal states of single atoms or (collective) excitations of atomic ensembles, with interactions mediated via their electronically highlyexcited Rydberg states (Rydberg-interacting qubits, or Rydberg qubits for short).

Ultracold Rydberg quantum systems have proven very successful for many-body physics and analog quantum simulation, and are now emerging as a competitive platform for digital quantum simulation and scalable quantum computing.

In this article we summarize the key features of the Rydberg platform as it stands today, emphasizing its versatility for engineering quantum logic gates and manybody Hamiltonians.

Ground-Rydberg (gr) qubits

The simplest class of Rydberg qubits are composed of one weakly-interacting state |gi ≡ |0 $\rangle$ and one strongly interacting Rydberg state |r ≡ |1 $\rangle$ (gr-qubits).

Rydberg-Rydberg (rr) qubits

Qubits encoded using two different Rydberg states (rr qubits) $\left|r'\right\rangle\equiv\left|0\right\rangle,\left|r\right\rangle\equiv\left|1\right\rangle$

Ground-ground (gg) qubits

Qubits encoded in two long-lived low-lying atomic states offer the best performance in terms of coherence times combined with switchable interactions, making them good candidates for universal quantum computing.

$|g\rangle\equiv|0\rangle,|g^{\prime}\rangle\equiv|1\rangle $