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Atomic energy level

Explanation of atomic energy level.
© Keio University

The simplest quantum system is the hydrogen atom, with a single proton for a nucleus and a single electron orbiting it. In an undergraduate quantum mechanics course, students are often asked to derive its size and behavior using Schroedinger’s equation. The position of the electron isn’t fixed, like a satellite in an orbit, but instead is a quantum probability wave in a standing wave of the kind we studied in the first week, known as an orbital. For an isolated hydrogen atom, both the ground and excited states derive from the simplest standing wave we demonstrated, and are spherical. For most atoms, the shapes are more complex, as they represent standing waves with a larger number of waves.

Simple energy levels

An atom has a minimum energy level, which we call the ground state. If it has absorbed energy from the environment, usually by absorbing a photon, we say that the atom is in an excited state. It will eventually release that energy by emitting a photon whose wavelength is determined by the amount of energy released. The atom can only be in one of a fixed set of energy levels, so it always emits a photon of a particular wavelength as it moves from one state to another. Starting in the ground state and absorbing smallest possible amount of energy, we say it moves to the first excited state. Second and higher excited states are possible, too.

We can create a qubit using the ground state and the first excited state. Just like we used the up and down arrows when talking about spin, we can write (g) and (e) inside our kets to describe the physical phenomenon, then map those states to data values for our computations. We can use the ground state (|grangle) as our (|0rangle) state, and (|erangle) as our (|1rangle) state.

Hyperfine levels

Ground and excited states have the advantage of being conceptually simple, but a second approach is also common. In the presence of magnetic fields, the behavior of an atom is more complex than we just described, especially when the atom has more protons in its nucleus and more electrons than a hydrogen atom. The energy level is primarily defined by the distance between the nucleus and the electron, but magnetic fields distort the shape of the nucleus and the electron’s orbital. Our single, well-defined energy level “splits” into two or more slightly different energy levels.

Because the energy levels of the hyperfine states are very close together, it takes less energy to move the qubit from one state to the other. We can use microwaves to control hyperfine states, rather than laser light.

We will discuss the strengths and weaknesses further when we discuss ion trap hardware.


最も単純な量子系は、水素原子です。水素原子は、核になっている1つの陽子とそれを中心に周回する1つの電子で構成されます。学部課程の量子力学の講義では、学生はシュレーディンガー方程式を使ってその大きさと振る舞いを導き出すことをよく求められます。電子の位置は、衛星の軌道のように固定されている訳ではなく、最初の週で学んだような定在波の量子確率波の軌道です。孤立した水素原子の場合、基底状態と励起状態の両方は、すでに学んだ最も単純な定常波から導出でき、球状です。 ほとんどの原子の場合、形状はより大きい波数を有する定在波を示すので、より複雑です。


原子には最小エネルギー準位があり、それを基底状態と呼びます。原子が光子を吸収するなどして環境からエネルギーを吸収した場合、原子は励起状態にあると言います。最終的に、光子を放出することによってそのエネルギーを放出します。このとき、放出するエネルギーの量によって放出する光の波長が決定されます。原子は固定されたエネルギー準位のセットのうちの1つにしか収まらないので、ある状態から別のある状態に移動する際に、常に特定の波長の光子を放出します。 初期状態が基底状態の原子が可能な値のなかで最も小さいエネルギー量を吸収すると、第一励起状態に移行すると言います。 第二やそれ以上の励起状態も存在します。

基底状態と第一励起状態を使って量子ビットを作ることができます。スピンにおいて上下の矢印を使用したのと同じように、物理的な現象を記述するときにケットの中に(g)(ground, 基底)と(e)(excited, 励起)を書くことができます。そして、それらの状態を、計算に利用するデータの値にマップし、(vert grangle)を(vert0rangle)、(vert erangle)を(vert1rangle)として扱うことができます。




超微細状態のエネルギー準位はそれぞれ非常に近いため、量子ビットをある状態から他の状態に移動させるのに必要なエネルギーは少なくて済みます。 私たちはレーザー光よりもむしろ超微細状態を制御するために、マイクロ波を使用します。


© Keio University
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Understanding Quantum Computers

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